Callable

You can annotate callables as a part of a type or an interface as follows

interface ReturnString {
  (): string
}

An instance of such an interface would be a function that returns a string e.g.

declare const foo: ReturnString;
const bar = foo(); // bar is inferred as a string

Obvious examples

Of course such a callable annotation can also specify any arguments / optional arguments / rest arguments as needed. e.g. here is a complex example:

interface Complex {
  (foo: string, bar?: number, ...others: boolean[]): number;
}

They can even specify overloads:

interface Overloaded {
  (foo: string): string
  (foo: number): number
}

// example implementation
const overloaded: Overloaded = (foo) => foo;

// example usage
const str = overloaded(''); // str is inferred string
const number = overloaded(123); // num is inferred number

Of course like all bodies of interfaces / types you can use these as variable type annotations e.g.

const overloaded: {
  (foo: string): string
  (foo: number): number
} = (foo) => foo;

Arrow Syntax

To make it easy to specify callable signatures TypeScript also allows simple arrow type annotations e.g. a function that takes a number and returns a string can be annotated as:

const simple: (foo: number) => string
    = (foo) => foo.toString();

Only limitation of the arrow syntax: You can't specify overloads. For overloads you must use the full bodied { (someArgs): someReturn } syntax.

Newable

Newable is just a special type of callable type annotation with the prefix new. It simply means that you need to invoke with new e.g.

interface CallMeWithNewToGetString {
  new(): string
}
// Usage 
declare const Foo: CallMeWithNewToGetString;
const bar = new Foo(); // bar is inferred to be of type string