diff --git a/types/backbone/index.d.ts b/types/backbone/index.d.ts
index 806086943e..42a322e4c2 100644
--- a/types/backbone/index.d.ts
+++ b/types/backbone/index.d.ts
@@ -219,7 +219,7 @@ declare namespace Backbone {
         /**
          * Specify a model attribute name (string) or function that will be used to sort the collection.
          */
-        comparator: string | ((element: TModel) => number | string) | ((compare: TModel, to?: TModel) => number);
+        comparator: string | { bivarianceHack(element: TModel): number | string }["bivarianceHack"] | { bivarianceHack(compare: TModel, to?: TModel): number }["bivarianceHack"];
 
         add(model: {}|TModel, options?: AddOptions): TModel;
         add(models: ({}|TModel)[], options?: AddOptions): TModel[];
diff --git a/types/bootbox/index.d.ts b/types/bootbox/index.d.ts
index ba5cc8c23b..c2fe427d6c 100644
--- a/types/bootbox/index.d.ts
+++ b/types/bootbox/index.d.ts
@@ -7,9 +7,9 @@
 /// <reference types="jquery" />
 
 /** Bootbox options shared by all modal types */
-interface BootboxBaseOptions {
+interface BootboxBaseOptions<T = any> {
 	title?: string | Element;
-	callback?: (result: boolean | string) => any;
+        callback?: (result: T) => any;
 	onEscape?: (() => any) | boolean;
 	show?: boolean;
 	backdrop?: boolean;
@@ -22,24 +22,24 @@ interface BootboxBaseOptions {
 }
 
 /** Bootbox options available for custom modals */
-interface BootboxDialogOptions extends BootboxBaseOptions {
+interface BootboxDialogOptions<T = any> extends BootboxBaseOptions<T> {
 	message: string | Element;
 }
 
 /** Bootbox options available for alert modals */
-interface BootboxAlertOptions extends BootboxDialogOptions {
+interface BootboxAlertOptions extends BootboxDialogOptions<void> {
 	callback?: () => any;
 	buttons?: BootboxAlertButtonMap;
 }
 
 /** Bootbox options available for confirm modals */
-interface BootboxConfirmOptions extends BootboxDialogOptions {
+interface BootboxConfirmOptions extends BootboxDialogOptions<boolean> {
 	callback: (result: boolean) => any;
 	buttons?: BootboxConfirmPromptButtonMap;
 }
 
 /** Bootbox options available for prompt modals */
-interface BootboxPromptOptions extends BootboxBaseOptions {
+interface BootboxPromptOptions extends BootboxBaseOptions<string> {
 	title: string;
 	value?: string;
 	inputType?: "text" | "textarea" | "email" | "select" | "checkbox" | "date" | "time" | "number" | "password";
@@ -93,7 +93,7 @@ interface BootboxStatic {
 	prompt(message: string, callback: (result: string) => void): JQuery;
 	prompt(options: BootboxPromptOptions): JQuery;
 	dialog(message: string, callback?: (result: string) => void): JQuery;
-	dialog(options: BootboxDialogOptions): JQuery;
+	dialog(options: BootboxDialogOptions<string>): JQuery;
 	setDefaults(options: BootboxDefaultOptions): void;
 	hideAll(): void;
 
diff --git a/types/bootbox/tsconfig.json b/types/bootbox/tsconfig.json
index e9bedd04f7..3ac9d8b49d 100644
--- a/types/bootbox/tsconfig.json
+++ b/types/bootbox/tsconfig.json
@@ -8,6 +8,7 @@
         "noImplicitAny": true,
         "noImplicitThis": true,
         "strictNullChecks": false,
+        "strictFunctionTypes": true,
         "baseUrl": "../",
         "typeRoots": [
             "../"
@@ -20,4 +21,4 @@
         "index.d.ts",
         "bootbox-tests.ts"
     ]
-}
\ No newline at end of file
+}
diff --git a/types/cordova-plugin-inappbrowser/index.d.ts b/types/cordova-plugin-inappbrowser/index.d.ts
index b266fbab44..1cf2c67642 100644
--- a/types/cordova-plugin-inappbrowser/index.d.ts
+++ b/types/cordova-plugin-inappbrowser/index.d.ts
@@ -25,7 +25,7 @@ interface Window {
  * NOTE: The InAppBrowser window behaves like a standard web browser, and can't access Cordova APIs.
  */
 interface InAppBrowser extends Window {
-    onloadstart(type: InAppBrowserEvent): void;
+    onloadstart(type: Event): void;
     onloadstop(type: InAppBrowserEvent): void;
     onloaderror(type: InAppBrowserEvent): void;
     onexit(type: InAppBrowserEvent): void;
diff --git a/types/cordova-plugin-inappbrowser/tsconfig.json b/types/cordova-plugin-inappbrowser/tsconfig.json
index fc11c3516e..2e42f7997b 100644
--- a/types/cordova-plugin-inappbrowser/tsconfig.json
+++ b/types/cordova-plugin-inappbrowser/tsconfig.json
@@ -8,6 +8,7 @@
         "noImplicitAny": false,
         "noImplicitThis": true,
         "strictNullChecks": false,
+        "strictFunctionTypes": true,
         "baseUrl": "../",
         "typeRoots": [
             "../"
@@ -20,4 +21,4 @@
         "index.d.ts",
         "cordova-plugin-inappbrowser-tests.ts"
     ]
-}
\ No newline at end of file
+}
diff --git a/types/ibm-mobilefirst/index.d.ts b/types/ibm-mobilefirst/index.d.ts
index 4da0cbf3b1..2577b0972b 100644
--- a/types/ibm-mobilefirst/index.d.ts
+++ b/types/ibm-mobilefirst/index.d.ts
@@ -61,8 +61,8 @@ declare namespace WL {
         getHeader(name: any): string;
     }
     interface Options {
-        onSuccess?: (response: IResponse) => void;
-        onFailure?: (response: IResponse) => void;
+        onSuccess?(response: IResponse): void;
+        onFailure?(response: IResponse): void;
         invocationContext?: any;
     }
     interface ResponseHandler<T> {
diff --git a/types/ibm-mobilefirst/tsconfig.json b/types/ibm-mobilefirst/tsconfig.json
index 0e4e6e45d9..86307e821b 100644
--- a/types/ibm-mobilefirst/tsconfig.json
+++ b/types/ibm-mobilefirst/tsconfig.json
@@ -8,6 +8,7 @@
         "noImplicitAny": true,
         "noImplicitThis": true,
         "strictNullChecks": false,
+        "strictFunctionTypes": true,
         "baseUrl": "../",
         "typeRoots": [
             "../"
@@ -20,4 +21,4 @@
         "index.d.ts",
         "ibm-mobilefirst-tests.ts"
     ]
-}
\ No newline at end of file
+}
diff --git a/types/q/q-tests.ts b/types/q/q-tests.ts
index cb9e46e5a7..f54f913e07 100644
--- a/types/q/q-tests.ts
+++ b/types/q/q-tests.ts
@@ -144,13 +144,13 @@ const nodeStyle = (input: string, cb: (error: any, success: any) => void) => {
 	cb(null, input);
 };
 
-Q.nfapply(nodeStyle, ["foo"]).done((result: string) => {
+Q.nfapply<string>(nodeStyle, ["foo"]).done((result: string) => {
 });
-Q.nfcall(nodeStyle, "foo").done((result: string) => {
+Q.nfcall<string>(nodeStyle, "foo").done((result: string) => {
 });
-Q.denodeify(nodeStyle)('foo').done((result: string) => {
+Q.denodeify<string>(nodeStyle)('foo').done((result: string) => {
 });
-Q.nfbind(nodeStyle)('foo').done((result: string) => {
+Q.nfbind<string>(nodeStyle)('foo').done((result: string) => {
 });
 
 class Repo {
@@ -171,7 +171,7 @@ class Repo {
 }
 
 const kitty = new Repo();
-Q.nbind(kitty.find, kitty)({cute: true}).done((kitties: any[]) => {
+Q.nbind<any[]>(kitty.find, kitty)({cute: true}).done((kitties: any[]) => {
 });
 
 /**
diff --git a/types/q/tsconfig.json b/types/q/tsconfig.json
index 12c105d622..40c079d929 100644
--- a/types/q/tsconfig.json
+++ b/types/q/tsconfig.json
@@ -8,6 +8,7 @@
         "noImplicitAny": true,
         "noImplicitThis": true,
         "strictNullChecks": false,
+        "strictFunctionTypes": true,
         "baseUrl": "../",
         "typeRoots": [
             "../"
diff --git a/types/react/index.d.ts b/types/react/index.d.ts
index 56d417319a..f7ce03ec91 100644
--- a/types/react/index.d.ts
+++ b/types/react/index.d.ts
@@ -72,7 +72,7 @@ declare namespace React {
     type ComponentType<P = {}> = ComponentClass<P> | StatelessComponent<P>;
 
     type Key = string | number;
-    type Ref<T> = string | ((instance: T | null) => any);
+    type Ref<T> = string | { bivarianceHack(instance: T | null): any }["bivarianceHack"];
 
     // tslint:disable-next-line:interface-over-type-literal
     type ComponentState = {};
@@ -555,7 +555,7 @@ declare namespace React {
     // Event Handler Types
     // ----------------------------------------------------------------------
 
-    type EventHandler<E extends SyntheticEvent<any>> = (event: E) => void;
+    type EventHandler<E extends SyntheticEvent<any>> = { bivarianceHack(event: E): void }["bivarianceHack"];
 
     type ReactEventHandler<T> = EventHandler<SyntheticEvent<T>>;
 
@@ -3369,7 +3369,7 @@ declare namespace React {
     // React.PropTypes
     // ----------------------------------------------------------------------
 
-    type Validator<T> = (object: T, key: string, componentName: string, ...rest: any[]) => Error | null;
+    type Validator<T> = { bivarianceHack(object: T, key: string, componentName: string, ...rest: any[]): Error | null }["bivarianceHack"];
 
     interface Requireable<T> extends Validator<T> {
         isRequired: Validator<T>;
diff --git a/types/react/tsconfig.json b/types/react/tsconfig.json
index d2c4600811..4c27ed5e21 100644
--- a/types/react/tsconfig.json
+++ b/types/react/tsconfig.json
@@ -14,6 +14,7 @@
         "noImplicitAny": true,
         "noImplicitThis": false,
         "strictNullChecks": true,
+        "strictFunctionTypes": true,
         "baseUrl": "../",
         "typeRoots": [
             "../"