Typescript – JSX element type ‘XXX’ does not have any construct or call signatures

This is a confusion between constructors and instances.

Remember that when you write a component in React:

class Greeter extends React.Component<any, any> {
    render() {
        return <div>Hello, {this.props.whoToGreet}</div>;
    }
}

You use it this way:

return <Greeter whoToGreet='world' />;

You don't use it this way:

let Greet = new Greeter();
return <Greet whoToGreet='world' />;

In the first example, we're passing around Greeter, the constructor function for our component. That's the correct usage. In the second example, we're passing around an instance of Greeter. That's incorrect, and will fail at runtime with an error like "Object is not a function".

The problem with this code

function renderGreeting(Elem: React.Component<any, any>) {
    return <span>Hello, <Elem />!</span>;
}

is that it's expecting an instance of React.Component. What you want is a function that takes a constructor for React.Component:

function renderGreeting(Elem: new() => React.Component<any, any>) {
    return <span>Hello, <Elem />!</span>;
}

or similarly:

function renderGreeting(Elem: typeof React.Component) {
    return <span>Hello, <Elem />!</span>;
}

Late to the party, with "@types/react-router-dom": "^4.3.4" and "@types/react": "16.9.1", and if you're using RouteProps, you will probably get the same error.

JSX element type 'Component' does not have any construct or call signatures. [2604]

That's because, in the RouteProps interface, the component is defined as optional, hence it might be undefined.

export interface RouteProps {
  location?: H.Location;
  component?: React.ComponentType<RouteComponentProps<any>> | React.ComponentType<any>;
  render?: ((props: RouteComponentProps<any>) => React.ReactNode);
  children?: ((props: RouteChildrenProps<any>) => React.ReactNode) | React.ReactNode;
  path?: string | string[];
  exact?: boolean;
  sensitive?: boolean;
  strict?: boolean;
}

Simply check for if the component is falsy will fix it.

function PrivateRoute({ component: Component, ...rest }: RouteProps) {
  if (!Component) return null;
  return (
    <Route
      {...rest}
      render={props =>
        fakeAuth.isAuthenticated ? (
          <Component {...props} />
        ) : (
          <Redirect
            to={{
              pathname: "/login",
              state: { from: props.location }
            }}
          />
        )
      }
    />
  );
}