diff --git a/.changeset/four-ghosts-sniff.md b/.changeset/four-ghosts-sniff.md
new file mode 100644
index 0000000000..9da0ab15ed
--- /dev/null
+++ b/.changeset/four-ghosts-sniff.md
@@ -0,0 +1,5 @@
+---
+'@backstage/core-plugin-api': minor
+---
+
+Removed the deprecated `OldIconComponent` type.
diff --git a/.changeset/twelve-bears-fail.md b/.changeset/twelve-bears-fail.md
new file mode 100644
index 0000000000..6112f5a980
--- /dev/null
+++ b/.changeset/twelve-bears-fail.md
@@ -0,0 +1,6 @@
+---
+'@backstage/core-app-api': patch
+'@backstage/core-plugin-api': patch
+---
+
+Removed direct and transitive MUI dependencies.
diff --git a/packages/core-app-api/package.json b/packages/core-app-api/package.json
index fe9c419d5d..de7477771f 100644
--- a/packages/core-app-api/package.json
+++ b/packages/core-app-api/package.json
@@ -29,15 +29,10 @@
     "clean": "backstage-cli clean"
   },
   "dependencies": {
-    "@backstage/app-defaults": "^0.1.3",
-    "@backstage/core-components": "^0.8.3",
     "@backstage/config": "^0.1.11",
     "@backstage/core-plugin-api": "^0.4.1",
-    "@backstage/theme": "^0.2.14",
     "@backstage/types": "^0.1.1",
     "@backstage/version-bridge": "^0.1.1",
-    "@material-ui/core": "^4.12.2",
-    "@material-ui/icons": "^4.9.1",
     "@types/prop-types": "^15.7.3",
     "prop-types": "^15.7.2",
     "react-router-dom": "6.0.0-beta.0",
diff --git a/packages/core-app-api/src/app/AppManager.tsx b/packages/core-app-api/src/app/AppManager.tsx
index ef5fe43b8b..d52e656559 100644
--- a/packages/core-app-api/src/app/AppManager.tsx
+++ b/packages/core-app-api/src/app/AppManager.tsx
@@ -49,7 +49,6 @@ import {
   SubRouteRef,
   ExternalRouteRef,
 } from '@backstage/core-plugin-api';
-import { UserIdentity } from '@backstage/core-components';
 import { ApiFactoryRegistry, ApiResolver } from '../apis/system';
 import {
   childDiscoverer,
@@ -360,7 +359,25 @@ export class AppManager implements BackstageApp {
 
       // If the app hasn't configured a sign-in page, we just continue as guest.
       if (!SignInPageComponent) {
-        this.appIdentityProxy.setTarget(UserIdentity.createGuest());
+        this.appIdentityProxy.setTarget({
+          getUserId: () => 'guest',
+          getIdToken: async () => undefined,
+          getProfile: () => ({
+            email: 'guest@example.com',
+            displayName: 'Guest',
+          }),
+          getProfileInfo: async () => ({
+            email: 'guest@example.com',
+            displayName: 'Guest',
+          }),
+          getBackstageIdentity: async () => ({
+            type: 'user',
+            userEntityRef: 'user:default/guest',
+            ownershipEntityRefs: ['user:default/guest'],
+          }),
+          getCredentials: async () => ({}),
+          signOut: async () => {},
+        });
 
         return (
           <RouterComponent>
diff --git a/packages/core-plugin-api/api-report.md b/packages/core-plugin-api/api-report.md
index 7a2fb95be8..de25d24660 100644
--- a/packages/core-plugin-api/api-report.md
+++ b/packages/core-plugin-api/api-report.md
@@ -16,7 +16,6 @@ import { ProfileInfo as ProfileInfo_2 } from '@backstage/core-plugin-api';
 import { default as React_2 } from 'react';
 import { ReactElement } from 'react';
 import { ReactNode } from 'react';
-import { SvgIconProps } from '@material-ui/core';
 
 // @public
 export type AlertApi = {
@@ -616,9 +615,6 @@ export const oktaAuthApiRef: ApiRef<
     SessionApi
 >;
 
-// @public @deprecated
-export type OldIconComponent = ComponentType<SvgIconProps>;
-
 // @alpha
 export const oneloginAuthApiRef: ApiRef<
   OAuthApi &
diff --git a/packages/core-plugin-api/package.json b/packages/core-plugin-api/package.json
index b7c9189394..d284d60c6b 100644
--- a/packages/core-plugin-api/package.json
+++ b/packages/core-plugin-api/package.json
@@ -30,10 +30,8 @@
   },
   "dependencies": {
     "@backstage/config": "^0.1.11",
-    "@backstage/theme": "^0.2.14",
     "@backstage/types": "^0.1.1",
     "@backstage/version-bridge": "^0.1.1",
-    "@material-ui/core": "^4.12.2",
     "history": "^5.0.0",
     "prop-types": "^15.7.2",
     "react-router-dom": "6.0.0-beta.0",
diff --git a/packages/core-plugin-api/src/icons/index.ts b/packages/core-plugin-api/src/icons/index.ts
index de79dd08d3..9c9e45e54c 100644
--- a/packages/core-plugin-api/src/icons/index.ts
+++ b/packages/core-plugin-api/src/icons/index.ts
@@ -14,4 +14,4 @@
  * limitations under the License.
  */
 
-export type { IconComponent, OldIconComponent } from './types';
+export type { IconComponent } from './types';
diff --git a/packages/core-plugin-api/src/icons/types.ts b/packages/core-plugin-api/src/icons/types.ts
index 849561f9c0..d7dca27bf9 100644
--- a/packages/core-plugin-api/src/icons/types.ts
+++ b/packages/core-plugin-api/src/icons/types.ts
@@ -15,7 +15,6 @@
  */
 
 import { ComponentType } from 'react';
-import { SvgIconProps } from '@material-ui/core';
 
 /**
  * IconComponent is the common icon type used throughout Backstage when
@@ -36,13 +35,3 @@ import { SvgIconProps } from '@material-ui/core';
 export type IconComponent = ComponentType<{
   fontSize?: 'default' | 'small' | 'large';
 }>;
-
-/**
- * This exists for backwards compatibility with the old core package.
- * It's used in some parts of this package in order to smooth out the
- * migration, but it is not exported.
- *
- * @public
- * @deprecated This type will be removed, use {@link IconComponent} instead.
- */
-export type OldIconComponent = ComponentType<SvgIconProps>;
diff --git a/plugins/catalog-react/api-report.md b/plugins/catalog-react/api-report.md
index 673d9256f1..66a496daff 100644
--- a/plugins/catalog-react/api-report.md
+++ b/plugins/catalog-react/api-report.md
@@ -310,7 +310,16 @@ export const EntityRefLink: React_2.ForwardRefExoticComponent<
     | 'children'
     | 'key'
     | 'id'
-    | 'classes'
+    | 'variant'
+    | 'state'
+    | 'href'
+    | 'download'
+    | 'hrefLang'
+    | 'ping'
+    | 'rel'
+    | 'target'
+    | 'type'
+    | 'referrerPolicy'
     | 'defaultChecked'
     | 'defaultValue'
     | 'suppressContentEditableWarning'
@@ -556,22 +565,13 @@ export const EntityRefLink: React_2.ForwardRefExoticComponent<
     | 'onTransitionEnd'
     | 'onTransitionEndCapture'
     | 'component'
-    | 'variant'
+    | 'classes'
     | 'innerRef'
-    | 'download'
-    | 'href'
-    | 'hrefLang'
-    | 'ping'
-    | 'rel'
-    | 'target'
-    | 'type'
-    | 'referrerPolicy'
     | 'noWrap'
     | 'gutterBottom'
     | 'paragraph'
     | 'align'
     | 'variantMapping'
-    | 'state'
     | 'TypographyClasses'
     | 'entityRef'
     | 'defaultKind'