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Pro Allows you to develop native apps
Pro Backed by Facebook
Facebook writes their mobile apps in React Native so the code base gets pretty thoroughly used in some highly demanding scenarios.
Pro More predictable control of the state
The one way data flow, makes it more predictable and easy to control.
Pro Can be used for web apps as well
Onsen UI is usable for classic web development as well as mobile.
Pro Open source and free
Onsen UI is open source, and completely free to use.
Pro Large selection of components
Onsen UI provides a wide selection of components that are ready to use out of the box and are easily customizable.
Pro Easy to use
Onsen UI provides very clear, well-written and detailed documentation.
It uses popular technologies that are likely already familiar to developers (such as jQuery and Angular).
The framework is semantic and intuitive to use, making it quite fast to learn.
Pro Supports React
React is the most trending front-end UI framework, naturally supporting that is a plus.
Con Steep learning curve
Con If core team doesn't use a certain feature, it's not developed
Whenever there's functionality you need that they don't use in their apps, it's not going to get developed by them, even if it's obvious it should be in the core. They always say to either submit a PR or create a separate module.