diff --git a/src/cdk/drag-drop/drag.spec.ts b/src/cdk/drag-drop/drag.spec.ts
index 10e8cce7f8d..c56a3526b64 100644
--- a/src/cdk/drag-drop/drag.spec.ts
+++ b/src/cdk/drag-drop/drag.spec.ts
@@ -567,6 +567,17 @@ describe('CdkDrag', () => {
       expect(dragElement.style.transform).toBe('translate3d(13px, 37px, 0px)');
     }));
 
+    it('should allow for dragging to be constrained to an element', fakeAsync(() => {
+      const fixture = createComponent(StandaloneDraggable);
+      fixture.componentInstance.boundarySelector = '.wrapper';
+      fixture.detectChanges();
+      const dragElement = fixture.componentInstance.dragElement.nativeElement;
+
+      expect(dragElement.style.transform).toBeFalsy();
+      dragElementViaMouse(fixture, dragElement, 300, 300);
+      expect(dragElement.style.transform).toBe('translate3d(100px, 100px, 0px)');
+    }));
+
   });
 
   describe('draggable with a handle', () => {
@@ -1057,6 +1068,29 @@ describe('CdkDrag', () => {
       expect(preview.parentNode).toBeFalsy('Expected preview to be removed from the DOM');
     }));
 
+    it('should be able to constrain the preview position', fakeAsync(() => {
+      const fixture = createComponent(DraggableInDropZone);
+      fixture.componentInstance.boundarySelector = '.cdk-drop-list';
+      fixture.detectChanges();
+      const item = fixture.componentInstance.dragItems.toArray()[1].element.nativeElement;
+      const listRect =
+          fixture.componentInstance.dropInstance.element.nativeElement.getBoundingClientRect();
+
+      startDraggingViaMouse(fixture, item);
+
+      const preview = document.querySelector('.cdk-drag-preview')! as HTMLElement;
+
+      startDraggingViaMouse(fixture, item, listRect.right + 50, listRect.bottom + 50);
+      flush();
+      dispatchMouseEvent(document, 'mousemove', listRect.right + 50, listRect.bottom + 50);
+      fixture.detectChanges();
+
+      const previewRect = preview.getBoundingClientRect();
+
+      expect(Math.floor(previewRect.bottom)).toBe(Math.floor(listRect.bottom));
+      expect(Math.floor(previewRect.right)).toBe(Math.floor(listRect.right));
+    }));
+
     it('should clear the id from the preview', fakeAsync(() => {
       const fixture = createComponent(DraggableInDropZone);
       fixture.detectChanges();
@@ -1108,7 +1142,7 @@ describe('CdkDrag', () => {
       preview.style.transitionDuration = '500ms';
 
       // Move somewhere so the draggable doesn't exit immediately.
-      dispatchTouchEvent(document, 'mousemove', 50, 50);
+      dispatchMouseEvent(document, 'mousemove', 50, 50);
       fixture.detectChanges();
 
       dispatchMouseEvent(document, 'mouseup');
@@ -1166,7 +1200,7 @@ describe('CdkDrag', () => {
       const preview = document.querySelector('.cdk-drag-preview')! as HTMLElement;
       preview.style.transition = 'opacity 500ms ease';
 
-      dispatchTouchEvent(document, 'mousemove', 50, 50);
+      dispatchMouseEvent(document, 'mousemove', 50, 50);
       fixture.detectChanges();
 
       dispatchMouseEvent(document, 'mouseup');
@@ -1188,7 +1222,7 @@ describe('CdkDrag', () => {
         const preview = document.querySelector('.cdk-drag-preview')! as HTMLElement;
         preview.style.transition = 'opacity 500ms ease, transform 1000ms ease';
 
-        dispatchTouchEvent(document, 'mousemove', 50, 50);
+        dispatchMouseEvent(document, 'mousemove', 50, 50);
         fixture.detectChanges();
 
         dispatchMouseEvent(document, 'mouseup');
@@ -1679,6 +1713,29 @@ describe('CdkDrag', () => {
       expect(preview.textContent!.trim()).toContain('Custom preview');
     }));
 
+    it('should be able to constrain the position of a custom preview', fakeAsync(() => {
+      const fixture = createComponent(DraggableInDropZoneWithCustomPreview);
+      fixture.componentInstance.boundarySelector = '.cdk-drop-list';
+      fixture.detectChanges();
+      const item = fixture.componentInstance.dragItems.toArray()[1].element.nativeElement;
+      const listRect =
+          fixture.componentInstance.dropInstance.element.nativeElement.getBoundingClientRect();
+
+      startDraggingViaMouse(fixture, item);
+
+      const preview = document.querySelector('.cdk-drag-preview')! as HTMLElement;
+
+      startDraggingViaMouse(fixture, item, listRect.right + 50, listRect.bottom + 50);
+      flush();
+      dispatchMouseEvent(document, 'mousemove', listRect.right + 50, listRect.bottom + 50);
+      fixture.detectChanges();
+
+      const previewRect = preview.getBoundingClientRect();
+
+      expect(Math.floor(previewRect.bottom)).toBe(Math.floor(listRect.bottom));
+      expect(Math.floor(previewRect.right)).toBe(Math.floor(listRect.right));
+    }));
+
     it('should revert the element back to its parent after dragging with a custom ' +
       'preview has stopped', fakeAsync(() => {
         const fixture = createComponent(DraggableInDropZoneWithCustomPreview);
@@ -2298,12 +2355,15 @@ describe('CdkDrag', () => {
 
 @Component({
   template: `
-    <div
-      cdkDrag
-      (cdkDragStarted)="startedSpy($event)"
-      (cdkDragEnded)="endedSpy($event)"
-      #dragElement
-      style="width: 100px; height: 100px; background: red;"></div>
+    <div class="wrapper" style="width: 200px; height: 200px; background: green;">
+      <div
+        cdkDrag
+        [cdkDragBoundary]="boundarySelector"
+        (cdkDragStarted)="startedSpy($event)"
+        (cdkDragEnded)="endedSpy($event)"
+        #dragElement
+        style="width: 100px; height: 100px; background: red;"></div>
+    </div>
   `
 })
 class StandaloneDraggable {
@@ -2311,6 +2371,7 @@ class StandaloneDraggable {
   @ViewChild(CdkDrag) dragInstance: CdkDrag;
   startedSpy = jasmine.createSpy('started spy');
   endedSpy = jasmine.createSpy('ended spy');
+  boundarySelector: string;
 }
 
 @Component({
@@ -2414,6 +2475,7 @@ const DROP_ZONE_FIXTURE_TEMPLATE = `
       *ngFor="let item of items"
       cdkDrag
       [cdkDragData]="item"
+      [cdkDragBoundary]="boundarySelector"
       [style.height.px]="item.height"
       [style.margin-bottom.px]="item.margin"
       style="width: 100%; background: red;">{{item.value}}</div>
@@ -2431,6 +2493,7 @@ class DraggableInDropZone {
     {value: 'Three', height: ITEM_HEIGHT, margin: 0}
   ];
   dropZoneId = 'items';
+  boundarySelector: string;
   sortedSpy = jasmine.createSpy('sorted spy');
   droppedSpy = jasmine.createSpy('dropped spy').and.callFake((event: CdkDragDrop<string[]>) => {
     moveItemInArray(this.items, event.previousIndex, event.currentIndex);
@@ -2493,10 +2556,16 @@ class DraggableInHorizontalDropZone {
 @Component({
   template: `
     <div cdkDropList style="width: 100px; background: pink;">
-      <div *ngFor="let item of items" cdkDrag
+      <div
+        *ngFor="let item of items"
+        cdkDrag
+        [cdkDragBoundary]="boundarySelector"
         style="width: 100%; height: ${ITEM_HEIGHT}px; background: red;">
           {{item}}
-          <div class="custom-preview" *cdkDragPreview>Custom preview</div>
+          <div
+            class="custom-preview"
+            style="width: 50px; height: 50px; background: purple;"
+            *cdkDragPreview>Custom preview</div>
       </div>
     </div>
   `
@@ -2505,6 +2574,7 @@ class DraggableInDropZoneWithCustomPreview {
   @ViewChild(CdkDropList) dropInstance: CdkDropList;
   @ViewChildren(CdkDrag) dragItems: QueryList<CdkDrag>;
   items = ['Zero', 'One', 'Two', 'Three'];
+  boundarySelector: string;
 }
 
 
diff --git a/src/cdk/drag-drop/drag.ts b/src/cdk/drag-drop/drag.ts
index 6ab2b357687..a5910622610 100644
--- a/src/cdk/drag-drop/drag.ts
+++ b/src/cdk/drag-drop/drag.ts
@@ -196,6 +196,15 @@ export class CdkDrag<T = any> implements AfterViewInit, OnDestroy {
   /** Subscription to the stream that initializes the root element. */
   private _rootElementInitSubscription = Subscription.EMPTY;
 
+  /** Cached reference to the boundary element. */
+  private _boundaryElement?: HTMLElement;
+
+  /** Cached dimensions of the preview element. */
+  private _previewRect?: ClientRect;
+
+  /** Cached dimensions of the boundary element. */
+  private _boundaryRect?: ClientRect;
+
   /** Elements that can be used to drag the draggable item. */
   @ContentChildren(CdkDragHandle, {descendants: true}) _handles: QueryList<CdkDragHandle>;
 
@@ -218,6 +227,13 @@ export class CdkDrag<T = any> implements AfterViewInit, OnDestroy {
    */
   @Input('cdkDragRootElement') rootElementSelector: string;
 
+  /**
+   * Selector that will be used to determine the element to which the draggable's position will
+   * be constrained. Matching starts from the element's parent and goes up the DOM until a matching
+   * element has been found.
+   */
+  @Input('cdkDragBoundary') boundaryElementSelector: string;
+
   /** Whether starting to drag this element is disabled. */
   @Input('cdkDragDisabled')
   get disabled(): boolean {
@@ -334,7 +350,7 @@ export class CdkDrag<T = any> implements AfterViewInit, OnDestroy {
     this._rootElementInitSubscription.unsubscribe();
     this._destroyPreview();
     this._destroyPlaceholder();
-    this._nextSibling = null;
+    this._boundaryElement = this._nextSibling = null!;
     this._dragDropRegistry.removeDragItem(this);
     this._removeSubscriptions();
     this._moveEvents.complete();
@@ -414,6 +430,11 @@ export class CdkDrag<T = any> implements AfterViewInit, OnDestroy {
     this._pointerMoveSubscription = this._dragDropRegistry.pointerMove.subscribe(this._pointerMove);
     this._pointerUpSubscription = this._dragDropRegistry.pointerUp.subscribe(this._pointerUp);
     this._scrollPosition = this._viewportRuler.getViewportScrollPosition();
+    this._boundaryElement = this._getBoundaryElement();
+
+    if (this._boundaryElement) {
+      this._boundaryRect = this._boundaryElement.getBoundingClientRect();
+    }
 
     // If we have a custom preview template, the element won't be visible anyway so we avoid the
     // extra `getBoundingClientRect` calls and just move the preview next to the cursor.
@@ -456,9 +477,8 @@ export class CdkDrag<T = any> implements AfterViewInit, OnDestroy {
 
   /** Handler that is invoked when the user moves their pointer after they've initiated a drag. */
   private _pointerMove = (event: MouseEvent | TouchEvent) => {
-    const pointerPosition = this._getConstrainedPointerPosition(event);
-
     if (!this._hasStartedDragging) {
+      const pointerPosition = this._getPointerPositionOnPage(event);
       const distanceX = Math.abs(pointerPosition.x - this._pickupPositionOnPage.x);
       const distanceY = Math.abs(pointerPosition.y - this._pickupPositionOnPage.y);
 
@@ -474,18 +494,28 @@ export class CdkDrag<T = any> implements AfterViewInit, OnDestroy {
       return;
     }
 
+    // We only need the preview dimensions if we have a boundary element.
+    if (this._boundaryElement) {
+      // Cache the preview element rect if we haven't cached it already or if
+      // we cached it too early before the element dimensions were computed.
+      if (!this._previewRect || (!this._previewRect.width && !this._previewRect.height)) {
+        this._previewRect = (this._preview || this._rootElement).getBoundingClientRect();
+      }
+    }
+
+    const constrainedPointerPosition = this._getConstrainedPointerPosition(event);
     this._hasMoved = true;
     event.preventDefault();
-    this._updatePointerDirectionDelta(pointerPosition);
+    this._updatePointerDirectionDelta(constrainedPointerPosition);
 
     if (this.dropContainer) {
-      this._updateActiveDropContainer(pointerPosition);
+      this._updateActiveDropContainer(constrainedPointerPosition);
     } else {
       const activeTransform = this._activeTransform;
       activeTransform.x =
-          pointerPosition.x - this._pickupPositionOnPage.x + this._passiveTransform.x;
+          constrainedPointerPosition.x - this._pickupPositionOnPage.x + this._passiveTransform.x;
       activeTransform.y =
-          pointerPosition.y - this._pickupPositionOnPage.y + this._passiveTransform.y;
+          constrainedPointerPosition.y - this._pickupPositionOnPage.y + this._passiveTransform.y;
       const transform = getTransform(activeTransform.x, activeTransform.y);
 
       // Preserve the previous `transform` value, if there was one.
@@ -506,7 +536,7 @@ export class CdkDrag<T = any> implements AfterViewInit, OnDestroy {
       this._ngZone.run(() => {
         this._moveEvents.next({
           source: this,
-          pointerPosition,
+          pointerPosition: constrainedPointerPosition,
           event,
           delta: this._pointerDirectionDelta
         });
@@ -560,6 +590,7 @@ export class CdkDrag<T = any> implements AfterViewInit, OnDestroy {
 
     this._destroyPreview();
     this._destroyPlaceholder();
+    this._boundaryRect = this._previewRect = undefined;
 
     // Re-enter the NgZone since we bound `document` events on the outside.
     this._ngZone.run(() => {
@@ -769,6 +800,19 @@ export class CdkDrag<T = any> implements AfterViewInit, OnDestroy {
       point.x = this._pickupPositionOnPage.x;
     }
 
+    if (this._boundaryRect) {
+      const {x: pickupX, y: pickupY} = this._pickupPositionInElement;
+      const boundaryRect = this._boundaryRect;
+      const previewRect = this._previewRect!;
+      const minY = boundaryRect.top + pickupY;
+      const maxY = boundaryRect.bottom - (previewRect.height - pickupY);
+      const minX = boundaryRect.left + pickupX;
+      const maxX = boundaryRect.right - (previewRect.width - pickupX);
+
+      point.x = clamp(point.x, minX, maxX);
+      point.y = clamp(point.y, minY, maxY);
+    }
+
     return point;
   }
 
@@ -832,22 +876,17 @@ export class CdkDrag<T = any> implements AfterViewInit, OnDestroy {
 
   /** Gets the root draggable element, based on the `rootElementSelector`. */
   private _getRootElement(): HTMLElement {
-    if (this.rootElementSelector) {
-      const selector = this.rootElementSelector;
-      let currentElement = this.element.nativeElement.parentElement as HTMLElement | null;
+    const element = this.element.nativeElement;
+    const rootElement = this.rootElementSelector ?
+        getClosestMatchingAncestor(element, this.rootElementSelector) : null;
 
-      while (currentElement) {
-        // IE doesn't support `matches` so we have to fall back to `msMatchesSelector`.
-        if (currentElement.matches ? currentElement.matches(selector) :
-            (currentElement as any).msMatchesSelector(selector)) {
-          return currentElement;
-        }
+    return rootElement || element;
+  }
 
-        currentElement = currentElement.parentElement;
-      }
-    }
-
-    return this.element.nativeElement;
+  /** Gets the boundary element, based on the `boundaryElementSelector`. */
+  private _getBoundaryElement() {
+    const selector = this.boundaryElementSelector;
+    return selector ? getClosestMatchingAncestor(this.element.nativeElement, selector) : undefined;
   }
 
   /** Unsubscribes from the global subscriptions. */
@@ -881,3 +920,23 @@ function deepCloneNode(node: HTMLElement): HTMLElement {
   clone.removeAttribute('id');
   return clone;
 }
+
+/** Clamps a value between a minimum and a maximum. */
+function clamp(value: number, min: number, max: number) {
+  return Math.max(min, Math.min(max, value));
+}
+
+/** Gets the closest ancestor of an element that matches a selector. */
+function getClosestMatchingAncestor(element: HTMLElement, selector: string) {
+  let currentElement = element.parentElement as HTMLElement | null;
+
+  while (currentElement) {
+    // IE doesn't support `matches` so we have to fall back to `msMatchesSelector`.
+    if (currentElement.matches ? currentElement.matches(selector) :
+        (currentElement as any).msMatchesSelector(selector)) {
+      return currentElement;
+    }
+
+    currentElement = currentElement.parentElement;
+  }
+}
diff --git a/tools/public_api_guard/cdk/drag-drop.d.ts b/tools/public_api_guard/cdk/drag-drop.d.ts
index 011421f7c27..8790915aeb4 100644
--- a/tools/public_api_guard/cdk/drag-drop.d.ts
+++ b/tools/public_api_guard/cdk/drag-drop.d.ts
@@ -10,6 +10,7 @@ export declare class CdkDrag<T = any> implements AfterViewInit, OnDestroy {
     _placeholderTemplate: CdkDragPlaceholder;
     _pointerDown: (event: TouchEvent | MouseEvent) => void;
     _previewTemplate: CdkDragPreview;
+    boundaryElementSelector: string;
     data: T;
     disabled: boolean;
     dropContainer: CdkDropListContainer;