If you're fascinated about "Universal JavaScript" code, there's enough in the making to get started.
We previously covered gl-react-native's OpenGL bindings for React Native and technics to share your application logic on web and mobile.

But today we're focusing on Components that can be shared between the web version of React and React Native, a concept that isn't something really new, but has been formalized since React v0.14.

We're obiouvsly talking about Components and code that don't depend on native features.
Here is a roundup of libraries and work that is in the making:

react-native-web (Nicolas Gallagher)

The core React Native components adapted and expanded upon for the web, backed by a precomputed CSS library

react-native-for-web (Mattia Manzati)

A set of classes and react components to make work your react-native app in a browser. (with some limitations obviously)

react-multiplatform (Les Orchard)

This is an experiment to build a React web app and a React Native iOS app that share as much as possible.