diff --git a/django/db/backends/schema.py b/django/db/backends/schema.py
index d282e0898b4..21eeefab824 100644
--- a/django/db/backends/schema.py
+++ b/django/db/backends/schema.py
@@ -272,7 +272,7 @@ class BaseDatabaseSchemaEditor(object):
             "new_tablespace": self.quote_name(new_db_tablespace),
         })
 
-    def create_field(self, model, field, keep_default=False):
+    def add_field(self, model, field, keep_default=False):
         """
         Creates a field on a model.
         Usually involves adding a column, but may involve adding a
@@ -325,7 +325,7 @@ class BaseDatabaseSchemaEditor(object):
                 }
             )
 
-    def delete_field(self, model, field):
+    def remove_field(self, model, field):
         """
         Removes a field from a model. Usually involves deleting a column,
         but for M2Ms may involve deleting a table.
diff --git a/django/db/backends/sqlite3/schema.py b/django/db/backends/sqlite3/schema.py
index de32dfd8936..19bffc75206 100644
--- a/django/db/backends/sqlite3/schema.py
+++ b/django/db/backends/sqlite3/schema.py
@@ -73,7 +73,7 @@ class DatabaseSchemaEditor(BaseDatabaseSchemaEditor):
         if restore_pk_field:
             restore_pk_field.primary_key = True
 
-    def create_field(self, model, field):
+    def add_field(self, model, field):
         """
         Creates a field on a model.
         Usually involves adding a column, but may involve adding a
@@ -89,7 +89,7 @@ class DatabaseSchemaEditor(BaseDatabaseSchemaEditor):
             raise ValueError("You cannot add a null=False column without a default value on SQLite.")
         self._remake_table(model, create_fields=[field])
 
-    def delete_field(self, model, field):
+    def remove_field(self, model, field):
         """
         Removes a field from a model. Usually involves deleting a column,
         but for M2Ms may involve deleting a table.
diff --git a/django/db/migrations/__init__.py b/django/db/migrations/__init__.py
index 154e7283413..e072786473f 100644
--- a/django/db/migrations/__init__.py
+++ b/django/db/migrations/__init__.py
@@ -1 +1,2 @@
 from .migration import Migration
+from .operations import *
diff --git a/django/db/migrations/graph.py b/django/db/migrations/graph.py
index 8d23b36cb70..8e2446ca991 100644
--- a/django/db/migrations/graph.py
+++ b/django/db/migrations/graph.py
@@ -1,4 +1,5 @@
 from django.utils.datastructures import SortedSet
+from django.db.migrations.state import ProjectState
 
 
 class MigrationGraph(object):
@@ -33,8 +34,10 @@ class MigrationGraph(object):
         self.nodes[node] = implementation
 
     def add_dependency(self, child, parent):
-        self.nodes[child] = None
-        self.nodes[parent] = None
+        if child not in self.nodes:
+            raise KeyError("Dependency references nonexistent child node %r" % (child,))
+        if parent not in self.nodes:
+            raise KeyError("Dependency references nonexistent parent node %r" % (parent,))
         self.dependencies.setdefault(child, set()).add(parent)
         self.dependents.setdefault(parent, set()).add(child)
 
@@ -117,6 +120,16 @@ class MigrationGraph(object):
     def __str__(self):
         return "Graph: %s nodes, %s edges" % (len(self.nodes), sum(len(x) for x in self.dependencies.values()))
 
+    def project_state(self, node):
+        """
+        Given a migration node, returns a complete ProjectState for it.
+        """
+        plan = self.forwards_plan(node)
+        project_state = ProjectState()
+        for node in plan:
+            project_state = self.nodes[node].mutate_state(project_state)
+        return project_state
+
 
 class CircularDependencyError(Exception):
     """
diff --git a/django/db/migrations/loader.py b/django/db/migrations/loader.py
index 4d191714cb4..ce9fb7c8dee 100644
--- a/django/db/migrations/loader.py
+++ b/django/db/migrations/loader.py
@@ -1,5 +1,6 @@
 import os
 from django.utils.importlib import import_module
+from django.utils.functional import cached_property
 from django.db.models.loading import cache
 from django.db.migrations.recorder import MigrationRecorder
 from django.db.migrations.graph import MigrationGraph
@@ -64,9 +65,10 @@ class MigrationLoader(object):
                 migration_module = import_module("%s.%s" % (module_name, migration_name))
                 if not hasattr(migration_module, "Migration"):
                     raise BadMigrationError("Migration %s in app %s has no Migration class" % (migration_name, app_label))
-                self.disk_migrations[app_label, migration_name] = migration_module.Migration
+                self.disk_migrations[app_label, migration_name] = migration_module.Migration(migration_name, app_label)
 
-    def build_graph(self):
+    @cached_property
+    def graph(self):
         """
         Builds a migration dependency graph using both the disk and database.
         """
@@ -116,6 +118,7 @@ class MigrationLoader(object):
         graph = MigrationGraph()
         for key, migration in normal.items():
             graph.add_node(key, migration)
+        for key, migration in normal.items():
             for parent in migration.dependencies:
                 graph.add_dependency(key, parent)
         return graph
diff --git a/django/db/migrations/migration.py b/django/db/migrations/migration.py
index afbcf65297d..a8b744a9b4e 100644
--- a/django/db/migrations/migration.py
+++ b/django/db/migrations/migration.py
@@ -10,6 +10,9 @@ class Migration(object):
      - dependencies: A list of tuples of (app_path, migration_name)
      - run_before: A list of tuples of (app_path, migration_name)
      - replaces: A list of migration_names
+
+    Note that all migrations come out of migrations and into the Loader or
+    Graph as instances, having been initialised with their app label and name.
     """
 
     # Operations to apply during this migration, in order.
@@ -28,3 +31,17 @@ class Migration(object):
     # non-empty, this migration will only be applied if all these migrations
     # are not applied.
     replaces = []
+
+    def __init__(self, name, app_label):
+        self.name = name
+        self.app_label = app_label
+
+    def mutate_state(self, project_state):
+        """
+        Takes a ProjectState and returns a new one with the migration's
+        operations applied to it.
+        """
+        new_state = project_state.clone()
+        for operation in self.operations:
+            operation.state_forwards(self.app_label, new_state)
+        return new_state
diff --git a/django/db/migrations/operations/__init__.py b/django/db/migrations/operations/__init__.py
index 4fb70b0418b..0aa7e2d119b 100644
--- a/django/db/migrations/operations/__init__.py
+++ b/django/db/migrations/operations/__init__.py
@@ -1 +1,2 @@
 from .models import CreateModel, DeleteModel
+from .fields import AddField, RemoveField
diff --git a/django/db/migrations/operations/base.py b/django/db/migrations/operations/base.py
index b24b45a09ae..f1b30d79f5d 100644
--- a/django/db/migrations/operations/base.py
+++ b/django/db/migrations/operations/base.py
@@ -15,21 +15,21 @@ class Operation(object):
     # Some operations are impossible to reverse, like deleting data.
     reversible = True
 
-    def state_forwards(self, app, state):
+    def state_forwards(self, app_label, state):
         """
         Takes the state from the previous migration, and mutates it
         so that it matches what this migration would perform.
         """
         raise NotImplementedError()
 
-    def database_forwards(self, app, schema_editor, from_state, to_state):
+    def database_forwards(self, app_label, schema_editor, from_state, to_state):
         """
         Performs the mutation on the database schema in the normal
         (forwards) direction.
         """
         raise NotImplementedError()
 
-    def database_backwards(self, app, schema_editor, from_state, to_state):
+    def database_backwards(self, app_label, schema_editor, from_state, to_state):
         """
         Performs the mutation on the database schema in the reverse
         direction - e.g. if this were CreateModel, it would in fact
diff --git a/django/db/migrations/operations/fields.py b/django/db/migrations/operations/fields.py
new file mode 100644
index 00000000000..2ecf77f7efa
--- /dev/null
+++ b/django/db/migrations/operations/fields.py
@@ -0,0 +1,52 @@
+from .base import Operation
+
+
+class AddField(Operation):
+    """
+    Adds a field to a model.
+    """
+
+    def __init__(self, model_name, name, instance):
+        self.model_name = model_name
+        self.name = name
+        self.instance = instance
+
+    def state_forwards(self, app_label, state):
+        state.models[app_label, self.model_name.lower()].fields.append((self.name, self.instance))
+
+    def database_forwards(self, app_label, schema_editor, from_state, to_state):
+        app_cache = to_state.render()
+        model = app_cache.get_model(app_label, self.name)
+        schema_editor.add_field(model, model._meta.get_field_by_name(self.name))
+
+    def database_backwards(self, app_label, schema_editor, from_state, to_state):
+        app_cache = from_state.render()
+        model = app_cache.get_model(app_label, self.name)
+        schema_editor.remove_field(model, model._meta.get_field_by_name(self.name))
+
+
+class RemoveField(Operation):
+    """
+    Removes a field from a model.
+    """
+
+    def __init__(self, model_name, name):
+        self.model_name = model_name
+        self.name = name
+
+    def state_forwards(self, app_label, state):
+        new_fields = []
+        for name, instance in state.models[app_label, self.model_name.lower()].fields:
+            if name != self.name:
+                new_fields.append((name, instance))
+        state.models[app_label, self.model_name.lower()].fields = new_fields
+
+    def database_forwards(self, app_label, schema_editor, from_state, to_state):
+        app_cache = from_state.render()
+        model = app_cache.get_model(app_label, self.name)
+        schema_editor.remove_field(model, model._meta.get_field_by_name(self.name))
+
+    def database_backwards(self, app_label, schema_editor, from_state, to_state):
+        app_cache = to_state.render()
+        model = app_cache.get_model(app_label, self.name)
+        schema_editor.add_field(model, model._meta.get_field_by_name(self.name))
diff --git a/django/db/migrations/operations/models.py b/django/db/migrations/operations/models.py
index fd709e26fa4..22d24f1eedc 100644
--- a/django/db/migrations/operations/models.py
+++ b/django/db/migrations/operations/models.py
@@ -1,4 +1,5 @@
 from .base import Operation
+from django.db import models
 from django.db.migrations.state import ModelState
 
 
@@ -7,20 +8,39 @@ class CreateModel(Operation):
     Create a model's table.
     """
 
-    def __init__(self, name):
+    def __init__(self, name, fields, options=None, bases=None):
         self.name = name
+        self.fields = fields
+        self.options = options or {}
+        self.bases = bases or (models.Model,)
 
-    def state_forwards(self, app, state):
-        state.models[app, self.name.lower()] = ModelState(state, app, self.name)
+    def state_forwards(self, app_label, state):
+        state.models[app_label, self.name.lower()] = ModelState(app_label, self.name, self.fields, self.options, self.bases)
 
     def database_forwards(self, app, schema_editor, from_state, to_state):
         app_cache = to_state.render()
         schema_editor.create_model(app_cache.get_model(app, self.name))
 
     def database_backwards(self, app, schema_editor, from_state, to_state):
-        """
-        Performs the mutation on the database schema in the reverse
-        direction - e.g. if this were CreateModel, it would in fact
-        drop the model's table.
-        """
-        raise NotImplementedError()
+        app_cache = from_state.render()
+        schema_editor.delete_model(app_cache.get_model(app, self.name))
+
+
+class DeleteModel(Operation):
+    """
+    Drops a model's table.
+    """
+
+    def __init__(self, name):
+        self.name = name
+
+    def state_forwards(self, app_label, state):
+        del state.models[app_label, self.name.lower()]
+
+    def database_forwards(self, app_label, schema_editor, from_state, to_state):
+        app_cache = from_state.render()
+        schema_editor.delete_model(app_cache.get_model(app_label, self.name))
+
+    def database_backwards(self, app_label, schema_editor, from_state, to_state):
+        app_cache = to_state.render()
+        schema_editor.create_model(app_cache.get_model(app_label, self.name))
diff --git a/django/db/migrations/state.py b/django/db/migrations/state.py
index 44ee1661218..d189e8709e4 100644
--- a/django/db/migrations/state.py
+++ b/django/db/migrations/state.py
@@ -21,7 +21,7 @@ class ProjectState(object):
     def clone(self):
         "Returns an exact copy of this ProjectState"
         return ProjectState(
-            models = dict((k, v.copy()) for k, v in self.models.items())
+            models = dict((k, v.clone()) for k, v in self.models.items())
         )
 
     def render(self):
@@ -49,12 +49,15 @@ class ModelState(object):
     mutate this one and then render it into a Model as required.
     """
 
-    def __init__(self, app_label, name, fields=None, options=None, bases=None):
+    def __init__(self, app_label, name, fields, options=None, bases=None):
         self.app_label = app_label
         self.name = name
-        self.fields = fields or []
+        self.fields = fields
         self.options = options or {}
         self.bases = bases or (models.Model, )
+        # Sanity-check that fields is NOT a dict. It must be ordered.
+        if isinstance(self.fields, dict):
+            raise ValueError("ModelState.fields cannot be a dict - it must be a list of 2-tuples.")
 
     @classmethod
     def from_model(cls, model):
diff --git a/tests/migrations/migrations/0001_initial.py b/tests/migrations/migrations/0001_initial.py
index bd613aa95e0..e2ed8559a66 100644
--- a/tests/migrations/migrations/0001_initial.py
+++ b/tests/migrations/migrations/0001_initial.py
@@ -1,5 +1,27 @@
-from django.db import migrations
+from django.db import migrations, models
 
 
 class Migration(migrations.Migration):
-    pass
+    
+    operations = [
+
+        migrations.CreateModel(
+            "Author",
+            [
+                ("id", models.AutoField(primary_key=True)),
+                ("name", models.CharField(max_length=255)),
+                ("slug", models.SlugField(null=True)),
+                ("age", models.IntegerField(default=0)),
+                ("silly_field", models.BooleanField()),
+            ],
+        ),
+
+        migrations.CreateModel(
+            "Tribble",
+            [
+                ("id", models.AutoField(primary_key=True)),
+                ("fluffy", models.BooleanField(default=True)),
+            ],
+        )
+        
+    ]
diff --git a/tests/migrations/migrations/0002_second.py b/tests/migrations/migrations/0002_second.py
index f4d3ba99021..fbaef11f714 100644
--- a/tests/migrations/migrations/0002_second.py
+++ b/tests/migrations/migrations/0002_second.py
@@ -1,6 +1,24 @@
-from django.db import migrations
+from django.db import migrations, models
 
 
 class Migration(migrations.Migration):
 
     dependencies = [("migrations", "0001_initial")]
+
+    operations = [
+
+        migrations.DeleteModel("Tribble"),
+
+        migrations.RemoveField("Author", "silly_field"),
+
+        migrations.AddField("Author", "important", models.BooleanField()),
+
+        migrations.CreateModel(
+            "Book",
+            [
+                ("id", models.AutoField(primary_key=True)),
+                ("author", models.ForeignKey("migrations.Author", null=True)),
+            ],
+        )
+
+    ]
diff --git a/tests/migrations/test_graph.py b/tests/migrations/test_graph.py
index b35d04fb8a9..207cc457414 100644
--- a/tests/migrations/test_graph.py
+++ b/tests/migrations/test_graph.py
@@ -1,11 +1,8 @@
-from django.test import TransactionTestCase, TestCase
-from django.db import connection
+from django.test import TestCase
 from django.db.migrations.graph import MigrationGraph, CircularDependencyError
-from django.db.migrations.loader import MigrationLoader
-from django.db.migrations.recorder import MigrationRecorder
 
 
-class GraphTests(TransactionTestCase):
+class GraphTests(TestCase):
     """
     Tests the digraph structure.
     """
@@ -117,20 +114,3 @@ class GraphTests(TransactionTestCase):
             CircularDependencyError,
             graph.forwards_plan, ("app_a", "0003"),
         )
-
-
-class LoaderTests(TransactionTestCase):
-    """
-    Tests the disk and database loader.
-    """
-
-    def test_load(self):
-        """
-        Makes sure the loader can load the migrations for the test apps.
-        """
-        migration_loader = MigrationLoader(connection)
-        graph = migration_loader.build_graph()
-        self.assertEqual(
-            graph.forwards_plan(("migrations", "0002_second")),
-            [("migrations", "0001_initial"), ("migrations", "0002_second")],
-        )
diff --git a/tests/migrations/test_loader.py b/tests/migrations/test_loader.py
index f8f31734f15..badace57cc6 100644
--- a/tests/migrations/test_loader.py
+++ b/tests/migrations/test_loader.py
@@ -1,11 +1,12 @@
-from django.test import TestCase
+from django.test import TestCase, TransactionTestCase
 from django.db import connection
+from django.db.migrations.loader import MigrationLoader
 from django.db.migrations.recorder import MigrationRecorder
 
 
 class RecorderTests(TestCase):
     """
-    Tests the disk and database loader.
+    Tests recording migrations as applied or not.
     """
 
     def test_apply(self):
@@ -27,3 +28,37 @@ class RecorderTests(TestCase):
             recorder.applied_migrations(),
             set(),
         )
+
+
+class LoaderTests(TransactionTestCase):
+    """
+    Tests the disk and database loader, and running through migrations
+    in memory.
+    """
+
+    def test_load(self):
+        """
+        Makes sure the loader can load the migrations for the test apps,
+        and then render them out to a new AppCache.
+        """
+        # Load and test the plan
+        migration_loader = MigrationLoader(connection)
+        self.assertEqual(
+            migration_loader.graph.forwards_plan(("migrations", "0002_second")),
+            [("migrations", "0001_initial"), ("migrations", "0002_second")],
+        )
+        # Now render it out!
+        project_state = migration_loader.graph.project_state(("migrations", "0002_second"))
+        self.assertEqual(len(project_state.models), 2)
+
+        author_state = project_state.models["migrations", "author"]
+        self.assertEqual(
+            [x for x, y in author_state.fields],
+            ["id", "name", "slug", "age", "important"]
+        )
+
+        book_state = project_state.models["migrations", "book"]
+        self.assertEqual(
+            [x for x, y in book_state.fields],
+            ["id", "author"]
+        )
diff --git a/tests/schema/tests.py b/tests/schema/tests.py
index 752f9a5d0b6..f643f3ed685 100644
--- a/tests/schema/tests.py
+++ b/tests/schema/tests.py
@@ -132,7 +132,7 @@ class SchemaTests(TransactionTestCase):
         else:
             self.fail("No FK constraint for author_id found")
 
-    def test_create_field(self):
+    def test_add_field(self):
         """
         Tests adding fields to models
         """
@@ -146,7 +146,7 @@ class SchemaTests(TransactionTestCase):
         new_field = IntegerField(null=True)
         new_field.set_attributes_from_name("age")
         with connection.schema_editor() as editor:
-            editor.create_field(
+            editor.add_field(
                 Author,
                 new_field,
             )
@@ -251,7 +251,7 @@ class SchemaTests(TransactionTestCase):
             connection.rollback()
             # Add the field
             with connection.schema_editor() as editor:
-                editor.create_field(
+                editor.add_field(
                     Author,
                     new_field,
                 )
@@ -260,7 +260,7 @@ class SchemaTests(TransactionTestCase):
             self.assertEqual(columns['tag_id'][0], "IntegerField")
             # Remove the M2M table again
             with connection.schema_editor() as editor:
-                editor.delete_field(
+                editor.remove_field(
                     Author,
                     new_field,
                 )
@@ -530,7 +530,7 @@ class SchemaTests(TransactionTestCase):
         )
         # Add a unique column, verify that creates an implicit index
         with connection.schema_editor() as editor:
-            editor.create_field(
+            editor.add_field(
                 Book,
                 BookWithSlug._meta.get_field_by_name("slug")[0],
             )
@@ -568,7 +568,7 @@ class SchemaTests(TransactionTestCase):
         new_field = SlugField(primary_key=True)
         new_field.set_attributes_from_name("slug")
         with connection.schema_editor() as editor:
-            editor.delete_field(Tag, Tag._meta.get_field_by_name("id")[0])
+            editor.remove_field(Tag, Tag._meta.get_field_by_name("id")[0])
             editor.alter_field(
                 Tag,
                 Tag._meta.get_field_by_name("slug")[0],