WebAuthn is supported in Firefox 60, and supported shortly in Chrome 67 and Edge 18, providing a cross-browser support that is the spiritual successor to U2F.

It's possible to migrate U2F users and their credentials to WebAuthn, but also possible to run U2F and WebAuthn side-by-side as separate modules.

MDN: https://developer.mozilla.org/en-US/docs/Web/API/Web_Authentication_API
Spec: https://www.w3.org/TR/webauthn/