diff --git a/src/cdk/overlay/overlay-directives.spec.ts b/src/cdk/overlay/overlay-directives.spec.ts
index 135e98e4965..0186577e1bc 100644
--- a/src/cdk/overlay/overlay-directives.spec.ts
+++ b/src/cdk/overlay/overlay-directives.spec.ts
@@ -359,6 +359,42 @@ describe('Overlay directives', () => {
       expect(Math.floor(overlayRect.left)).toBe(Math.floor(triggerRect.left) + 20);
     });
 
+    it('should be able to set the viewport margin', () => {
+      expect(fixture.componentInstance.connectedOverlayDirective.viewportMargin).not.toBe(10);
+
+      fixture.componentInstance.viewportMargin = 10;
+      fixture.detectChanges();
+
+      expect(fixture.componentInstance.connectedOverlayDirective.viewportMargin).toBe(10);
+    });
+
+    it('should allow for flexible positioning to be enabled', () => {
+      expect(fixture.componentInstance.connectedOverlayDirective.flexibleDiemsions).not.toBe(true);
+
+      fixture.componentInstance.flexibleDimensions = true;
+      fixture.detectChanges();
+
+      expect(fixture.componentInstance.connectedOverlayDirective.flexibleDiemsions).toBe(true);
+    });
+
+    it('should allow for growing after open to be enabled', () => {
+      expect(fixture.componentInstance.connectedOverlayDirective.growAfterOpen).not.toBe(true);
+
+      fixture.componentInstance.growAfterOpen = true;
+      fixture.detectChanges();
+
+      expect(fixture.componentInstance.connectedOverlayDirective.growAfterOpen).toBe(true);
+    });
+
+    it('should allow for pushing to be enabled', () => {
+      expect(fixture.componentInstance.connectedOverlayDirective.push).not.toBe(true);
+
+      fixture.componentInstance.push = true;
+      fixture.detectChanges();
+
+      expect(fixture.componentInstance.connectedOverlayDirective.push).toBe(true);
+    });
+
   });
 
   describe('outputs', () => {
@@ -421,6 +457,10 @@ describe('Overlay directives', () => {
             [cdkConnectedOverlayHeight]="height"
             [cdkConnectedOverlayOrigin]="triggerOverride || trigger"
             [cdkConnectedOverlayHasBackdrop]="hasBackdrop"
+            [cdkConnectedOverlayViewportMargin]="viewportMargin"
+            [cdkConnectedOverlayFlexibleDimensions]="flexibleDimensions"
+            [cdkConnectedOverlayGrowAfterOpen]="growAfterOpen"
+            [cdkConnectedOverlayPush]="push"
             cdkConnectedOverlayBackdropClass="mat-test-class"
             (backdropClick)="backdropClickHandler($event)"
             [cdkConnectedOverlayOffsetX]="offsetX"
@@ -448,6 +488,10 @@ class ConnectedOverlayDirectiveTest {
   offsetY: number;
   triggerOverride: CdkOverlayOrigin;
   hasBackdrop: boolean;
+  viewportMargin: number;
+  flexibleDimensions: boolean;
+  growAfterOpen: boolean;
+  push: boolean;
   backdropClickHandler = jasmine.createSpy('backdropClick handler');
   positionChangeHandler = jasmine.createSpy('positionChangeHandler');
   positionOverrides: ConnectionPositionPair[];
diff --git a/src/cdk/overlay/overlay-directives.ts b/src/cdk/overlay/overlay-directives.ts
index bdb203b0881..3a9c074fc3d 100644
--- a/src/cdk/overlay/overlay-directives.ts
+++ b/src/cdk/overlay/overlay-directives.ts
@@ -106,7 +106,8 @@ export class CdkOverlayOrigin {
 
 
 /**
- * Directive to facilitate declarative creation of an Overlay using a ConnectedPositionStrategy.
+ * Directive to facilitate declarative creation of an
+ * Overlay using a FlexibleConnectedPositionStrategy.
  */
 @Directive({
   selector: '[cdk-connected-overlay], [connected-overlay], [cdkConnectedOverlay]',
@@ -117,6 +118,9 @@ export class CdkConnectedOverlay implements OnDestroy, OnChanges {
   private _templatePortal: TemplatePortal;
   private _hasBackdrop = false;
   private _lockPosition = false;
+  private _growAfterOpen = false;
+  private _flexibleDimensions = false;
+  private _push = false;
   private _backdropSubscription = Subscription.EMPTY;
   private _offsetX: number;
   private _offsetY: number;
@@ -165,6 +169,9 @@ export class CdkConnectedOverlay implements OnDestroy, OnChanges {
   /** The custom class to be set on the backdrop element. */
   @Input('cdkConnectedOverlayBackdropClass') backdropClass: string;
 
+  /** Margin between the overlay and the viewport edges. */
+  @Input('cdkConnectedOverlayViewportMargin') viewportMargin: number = 0;
+
   /** Strategy to be used when handling scroll events while the overlay is open. */
   @Input('cdkConnectedOverlayScrollStrategy') scrollStrategy: ScrollStrategy =
       this._scrollStrategy();
@@ -182,6 +189,21 @@ export class CdkConnectedOverlay implements OnDestroy, OnChanges {
   get lockPosition() { return this._lockPosition; }
   set lockPosition(value: any) { this._lockPosition = coerceBooleanProperty(value); }
 
+  /** Whether the overlay's width and height can be constrained to fit within the viewport. */
+  @Input('cdkConnectedOverlayFlexibleDimensions')
+  get flexibleDiemsions() { return this._flexibleDimensions; }
+  set flexibleDiemsions(value: boolean) { this._flexibleDimensions = coerceBooleanProperty(value); }
+
+  /** Whether the overlay can grow after the initial open when flexible positioning is turned on. */
+  @Input('cdkConnectedOverlayGrowAfterOpen')
+  get growAfterOpen() { return this._growAfterOpen; }
+  set growAfterOpen(value: boolean) { this._growAfterOpen = coerceBooleanProperty(value); }
+
+  /** Whether the overlay can be pushed on-screen if none of the provided positions fit. */
+  @Input('cdkConnectedOverlayPush')
+  get push() { return this._push; }
+  set push(value: boolean) { this._push = coerceBooleanProperty(value); }
+
   /** Event emitted when the backdrop is clicked. */
   @Output() backdropClick = new EventEmitter<MouseEvent>();
 
@@ -288,13 +310,10 @@ export class CdkConnectedOverlay implements OnDestroy, OnChanges {
   private _createPositionStrategy(): FlexibleConnectedPositionStrategy {
     const strategy = this._overlay.position()
       .flexibleConnectedTo(this.origin.elementRef)
-      // Turn off all of the flexible positioning features for now to have it behave
-      // the same way as the old ConnectedPositionStrategy and to avoid breaking changes.
-      // TODO(crisbeto): make these on by default and add inputs for them
-      // next time we do breaking changes.
-      .withFlexibleDimensions(false)
-      .withPush(false)
-      .withGrowAfterOpen(false)
+      .withFlexibleDimensions(this.flexibleDiemsions)
+      .withPush(this.push)
+      .withGrowAfterOpen(this.growAfterOpen)
+      .withViewportMargin(this.viewportMargin)
       .withLockedPosition(this.lockPosition);
 
     this._setPositions(strategy);
diff --git a/src/cdk/overlay/position/flexible-connected-position-strategy.ts b/src/cdk/overlay/position/flexible-connected-position-strategy.ts
index 941bed23865..a793cb568f2 100644
--- a/src/cdk/overlay/position/flexible-connected-position-strategy.ts
+++ b/src/cdk/overlay/position/flexible-connected-position-strategy.ts
@@ -137,7 +137,7 @@ export class FlexibleConnectedPositionStrategy implements PositionStrategy {
     overlayRef.hostElement.classList.add('cdk-overlay-connected-position-bounding-box');
 
     this._overlayRef = overlayRef;
-    this._boundingBox = overlayRef.hostElement!;
+    this._boundingBox = overlayRef.hostElement;
     this._pane = overlayRef.overlayElement;
     this._resizeSubscription.unsubscribe();
     this._resizeSubscription = this._viewportRuler.change().subscribe(() => this.apply());