I spent a large part of the development on the animations. Reapp has a custom animation mixin designed for React that works through props. It's really cool and I'll be writing a blog post on it this week. It's what drives all the animations you see including the fully interactive "swipe view from edge to go back", as well as modals and popovers. You can see the animations here:
https://github.com/reapp/reapp-ui/blob/master/themes/ios/ani...
Another thing I've spent a lot of time on was getting the view animations to match iOS. Notice how the TitleBar text animates, while the icons remain in the same position. This took quite a bit of effort and resulted in several refactors of the animation library.
Finally, theming. The theme system is quite robust, though the iOS theme itself needs work. It's fully JS-powered CSS, and we use Flexbox for the default theme. It uses two teirs: Constants and Styles. You can override any of our constants or styles to make your own theme, or load an entire new one. I'll also be writing about this more because it's really a big feature. Here's an example of loading a custom theme:
https://github.com/reapp/hacker-news-app/blob/master/app/the...
That folder also contains more interesting usage.
Feel free to ask me any questions you all have, I'm happy to answer.