Jest and Enzyme are my preferred tools for testing React applications. They provide everything I need, from asserting, manupulating and traversing React components to snapshot testing.
I made the switch from Mocha to Jest lately and never looked back. Jest is simply amazing. The setup is seamless and the developer experience is outstanding - it's really fast, the continous testing capabilities are one of a kind, with the pattern matching and the specific test execution. Jest also comes with coverage tool out of the box with no additional configuration.
Enzyme is an utility library for working with React components. The API is quite extensive with support for shadow, static and full rendering. There are several Enzyme plugins like should-enzyme, expect-enzyme, jasmine-enzyme, etc. which extends the library's funtionality even more.