This is a must-watch. Cheng talks about what animations in React on the Web currently look like and the complexities that arise when building it out. He shows a few demos, including chat-heads and some neat slow-motion tricks.

https://www.youtube.com/watch?v=1tavDv5hXpo

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"Spencer Ahrens - React Native: Building Fluid User Experiences"

Spencer talks about the "Animated" API that currently landed for React Native. There is a mention that it's cross-platform (working on Android and iOS right now) and might be coming to the web soon (skip to @33min48s to get specifics). It's looking positive and he doesn't seem concerned about hitting "close parity" on the web.

https://www.youtube.com/watch?v=xDlfrcM6YBk

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React Native's new "Animated" API Docs

https://facebook.github.io/react-native/docs/animations.html