Note: you may have to install/upgrade/link Node.js and other parts of your environment in order for the tests to run correctly. Check out the latest setup in .travis.yml
React Native provides facilities to make it easier to test integrated components that require both native and JS components to communicate across the bridge. The two main components are RCTTestRunner and RCTTestModule. RCTTestRunner sets up the ReactNative environment and provides facilities to run the tests as XCTestCases in Xcode (runTest:module is the simplest method). RCTTestModule is exported to JS as NativeModules.TestModule. The tests themselves are written in JS, and must call TestModule.markTestCompleted() when they are done, otherwise the test will timeout and fail. Test failures are primarily indicated by throwing a JS exception. It is also possible to test error conditions with runTest:module:initialProps:expectErrorRegex: or runTest:module:initialProps:expectErrorBlock: which will expect an error to be thrown and verify the error matches the provided criteria. See IntegrationTestHarnessTest.js, IntegrationTests.m, and IntegrationTestsApp.js for example usage and integration points.
You can run integration tests locally with cmd+U in the IntegrationTest and UIExplorer apps in Xcode.
A common type of integration test is the snapshot test. These tests render a component, and verify snapshots of the screen against reference images using TestModule.verifySnapshot(), using the FBSnapshotTestCase library behind the scenes. Reference images are recorded by setting recordMode = YES on the RCTTestRunner, then running the tests. Snapshots will differ slightly between 32 and 64 bit, and various OS versions, so it's recommended that you enforce tests are run with the correct configuration. It's also highly recommended that all network data be mocked out, along with other potentially troublesome dependencies. See SimpleSnapshotTest for a basic example.
If you make a change that affects a snapshot test in a PR, such as adding a new example case to one of the examples that is snapshotted, you'll need to re-record the snapshotshot reference image. To do this, simply change to _runner.recordMode = YES; in UIExplorer/IntegrationTests.m, re-run the failing tests, then flip record back to NO and submit/update your PR and wait to see if the Travis build passes.