diff --git a/src/lib/stepper/step-header.html b/src/lib/stepper/step-header.html
index fac0b329b18c..2d35efdba267 100644
--- a/src/lib/stepper/step-header.html
+++ b/src/lib/stepper/step-header.html
@@ -3,15 +3,27 @@
      [class.mat-step-icon-not-touched]="state == 'number' && !selected"
      [ngSwitch]="state">
 
-  <span *ngSwitchCase="'number'">{{index + 1}}</span>
+  <ng-container *ngSwitchCase="'number'" [ngSwitch]="!!(iconOverrides && iconOverrides.number)">
+    <ng-container
+      *ngSwitchCase="true"
+      [ngTemplateOutlet]="iconOverrides.number"
+      [ngTemplateOutletContext]="_getIconContext()"></ng-container>
+    <span *ngSwitchDefault>{{index + 1}}</span>
+  </ng-container>
 
   <ng-container *ngSwitchCase="'edit'" [ngSwitch]="!!(iconOverrides && iconOverrides.edit)">
-    <ng-container *ngSwitchCase="true" [ngTemplateOutlet]="iconOverrides.edit"></ng-container>
+    <ng-container
+      *ngSwitchCase="true"
+      [ngTemplateOutlet]="iconOverrides.edit"
+      [ngTemplateOutletContext]="_getIconContext()"></ng-container>
     <mat-icon *ngSwitchDefault>create</mat-icon>
   </ng-container>
 
   <ng-container *ngSwitchCase="'done'" [ngSwitch]="!!(iconOverrides && iconOverrides.done)">
-    <ng-container *ngSwitchCase="true" [ngTemplateOutlet]="iconOverrides.done"></ng-container>
+    <ng-container
+      *ngSwitchCase="true"
+      [ngTemplateOutlet]="iconOverrides.done"
+      [ngTemplateOutletContext]="_getIconContext()"></ng-container>
     <mat-icon *ngSwitchDefault>done</mat-icon>
   </ng-container>
 </div>
diff --git a/src/lib/stepper/step-header.ts b/src/lib/stepper/step-header.ts
index 13157c34e7a7..66adfff9f0a5 100644
--- a/src/lib/stepper/step-header.ts
+++ b/src/lib/stepper/step-header.ts
@@ -20,6 +20,7 @@ import {
 import {Subscription} from 'rxjs/Subscription';
 import {MatStepLabel} from './step-label';
 import {MatStepperIntl} from './stepper-intl';
+import {MatStepperIconContext} from './stepper-icon';
 
 
 @Component({
@@ -44,7 +45,7 @@ export class MatStepHeader implements OnDestroy {
   @Input() label: MatStepLabel | string;
 
   /** Overrides for the header icons, passed in via the stepper. */
-  @Input() iconOverrides: {[key: string]: TemplateRef<any>};
+  @Input() iconOverrides: {[key: string]: TemplateRef<MatStepperIconContext>};
 
   /** Index of the given step. */
   @Input() index: number;
@@ -87,6 +88,15 @@ export class MatStepHeader implements OnDestroy {
     return this._element.nativeElement;
   }
 
+  /** Template context variables that are exposed to the `matStepperIcon` instances. */
+  _getIconContext(): MatStepperIconContext {
+    return {
+      index: this.index,
+      active: this.active,
+      optional: this.optional
+    };
+  }
+
   focus() {
     this._getHostElement().focus();
   }
diff --git a/src/lib/stepper/stepper-icon.ts b/src/lib/stepper/stepper-icon.ts
index b2bf79fe14d1..c8cc8556072e 100644
--- a/src/lib/stepper/stepper-icon.ts
+++ b/src/lib/stepper/stepper-icon.ts
@@ -8,6 +8,16 @@
 
 import {Directive, Input, TemplateRef} from '@angular/core';
 
+/** Template context available to an attached `matStepperIcon`. */
+export interface MatStepperIconContext {
+  /** Index of the step. */
+  index: number;
+  /** Whether the step is currently active. */
+  active: boolean;
+  /** Whether the step is optional. */
+  optional: boolean;
+}
+
 /**
  * Template to be used to override the icons inside the step header.
  */
@@ -16,7 +26,7 @@ import {Directive, Input, TemplateRef} from '@angular/core';
 })
 export class MatStepperIcon {
   /** Name of the icon to be overridden. */
-  @Input('matStepperIcon') name: 'edit' | 'done';
+  @Input('matStepperIcon') name: 'edit' | 'done' | 'number';
 
-  constructor(public templateRef: TemplateRef<any>) { }
+  constructor(public templateRef: TemplateRef<MatStepperIconContext>) {}
 }
diff --git a/src/lib/stepper/stepper.md b/src/lib/stepper/stepper.md
index 37ac9a30d3b4..d8fafef1eef3 100644
--- a/src/lib/stepper/stepper.md
+++ b/src/lib/stepper/stepper.md
@@ -124,7 +124,8 @@ this default `completed` behavior by setting the `completed` attribute as needed
 #### Overriding icons
 By default, the step headers will use the `create` and `done` icons from the Material design icon
 set via `<mat-icon>` elements. If you want to provide a different set of icons, you can do so
-by placing a `matStepperIcon` for each of the icons that you want to override:
+by placing a `matStepperIcon` for each of the icons that you want to override. The `index`,
+`active`, and `optional` values of the individual steps are available through template variables:
 
 ```html
 <mat-vertical-stepper>
@@ -136,6 +137,11 @@ by placing a `matStepperIcon` for each of the icons that you want to override:
     <mat-icon>done_all</mat-icon>
   </ng-template>
 
+  <!-- Custom icon with a context variable. -->
+  <ng-template matStepperIcon="number" let-index="index">
+    {{index + 10}}
+  </ng-template>
+
   <!-- Stepper steps go here -->
 </mat-vertical-stepper>
 ```
diff --git a/src/lib/stepper/stepper.spec.ts b/src/lib/stepper/stepper.spec.ts
index e3198496c70c..57c964336512 100644
--- a/src/lib/stepper/stepper.spec.ts
+++ b/src/lib/stepper/stepper.spec.ts
@@ -354,6 +354,13 @@ describe('MatStepper', () => {
 
       expect(header.textContent).toContain('Custom done');
     });
+
+    it('should allow for the `number` icon to be overridden with context', () => {
+      const stepperDebugElement = fixture.debugElement.query(By.directive(MatStepper));
+      const headers = stepperDebugElement.nativeElement.querySelectorAll('mat-step-header');
+
+      expect(headers[2].textContent).toContain('III');
+    });
   });
 
   describe('RTL', () => {
@@ -1025,6 +1032,9 @@ class SimpleStepperWithStepControlAndCompletedBinding {
     <mat-horizontal-stepper>
       <ng-template matStepperIcon="edit">Custom edit</ng-template>
       <ng-template matStepperIcon="done">Custom done</ng-template>
+      <ng-template matStepperIcon="number" let-index="index">
+        {{getRomanNumeral(index + 1)}}
+      </ng-template>
 
       <mat-step>Content 1</mat-step>
       <mat-step>Content 2</mat-step>
@@ -1032,7 +1042,21 @@ class SimpleStepperWithStepControlAndCompletedBinding {
     </mat-horizontal-stepper>
 `
 })
-class IconOverridesStepper {}
+class IconOverridesStepper {
+  getRomanNumeral(value: number) {
+    return {
+      1: 'I',
+      2: 'II',
+      3: 'III',
+      4: 'IV',
+      5: 'V',
+      6: 'VI',
+      7: 'VII',
+      8: 'VIII',
+      9: 'IX'
+    }[value];
+  }
+}
 
 @Component({
   template: `
diff --git a/src/lib/stepper/stepper.ts b/src/lib/stepper/stepper.ts
index 3efd2f86121d..b51f2c78b1dc 100644
--- a/src/lib/stepper/stepper.ts
+++ b/src/lib/stepper/stepper.ts
@@ -31,7 +31,7 @@ import {takeUntil} from 'rxjs/operators/takeUntil';
 import {MatStepHeader} from './step-header';
 import {MatStepLabel} from './step-label';
 import {matStepperAnimations} from './stepper-animations';
-import {MatStepperIcon} from './stepper-icon';
+import {MatStepperIcon, MatStepperIconContext} from './stepper-icon';
 
 /** Workaround for https://github.com/angular/angular/issues/17849 */
 export const _MatStep = CdkStep;
@@ -83,20 +83,18 @@ export class MatStepper extends CdkStepper implements AfterContentInit {
   @ContentChildren(MatStepperIcon) _icons: QueryList<MatStepperIcon>;
 
   /** Consumer-specified template-refs to be used to override the header icons. */
-  _iconOverrides: {[key: string]: TemplateRef<any>} = {};
+  _iconOverrides: {[key: string]: TemplateRef<MatStepperIconContext>} = {};
 
   ngAfterContentInit() {
     const icons = this._icons.toArray();
-    const editOverride = icons.find(icon => icon.name === 'edit');
-    const doneOverride = icons.find(icon => icon.name === 'done');
 
-    if (editOverride) {
-      this._iconOverrides.edit = editOverride.templateRef;
-    }
+    ['edit', 'done', 'number'].forEach(name => {
+      const override = icons.find(icon => icon.name === name);
 
-    if (doneOverride) {
-      this._iconOverrides.done = doneOverride.templateRef;
-    }
+      if (override) {
+        this._iconOverrides[name] = override.templateRef;
+      }
+    });
 
     // Mark the component for change detection whenever the content children query changes
     this._steps.changes.pipe(takeUntil(this._destroyed)).subscribe(() => this._stateChanged());