Recs.
Updated
React can also act as a "widget toolkit" by using pre-made React components. http://react-components.com/
Specs
Pros
Pro Flux architecture pattern
Flux is a platform agnostic pattern which can technically be used with any application or programming language.
One of Flux' main features is that it enforces uni-directional data flow which means that views do not change the data directly.
With React this is useful because this way it's easier to understand an application as it starts getting more complicated. By having two-way data binding, lead to unpredictable changes, where changing one model's data would end up updating another model. By using the Flux architecture, this can be avoided.
Pro Good debugging tools
React has an official Chrome Extension which is used as a developing and debugging tool. It can be used to quickly and painlessly debug your application or view the whole application structure as it's rendered.
Cons
Con Large file size
React's react.min.js is 145.5KB in size. It's much larger than some other libraries that offer roughly the same features and it's almost the same size as some MV* frameworks such as Angular or Ember that offer more features out of the box.
Although, it should be mentioned that sometimes having a smaller library may force developers to reinvent the wheel and write inefficient implementations on features that React already has. Ending up with a larger application that's harder to maintain and/or that has bad performance.
Con You have to learn a new syntax
Requires to learn a custom syntax, JSX that has some gotchas and introduce complexity, a steeper learning curve, and incompatibility with other tools.
Though you can opt out from JSX and use vanilla JS instead. But that is not recommended since it adds a lot of unneeded complexity which JSX tries to avoid.
Con No support for legacy browsers
React has recently dropped support for Internet Explorer 8. While the library may still work on IE8, issues that affect only IE8 will not be prioritized and/or solved.