Internally, we had no problems and didn't have to make any changes for this upgrade. If you're curious, you can check out the webpack changelog for 3.0.0 and 3.1.0.
Internally, we used jsdom-global to inject global.document, global.window and other DOM API into our Jest tests. After the upgrade we saw some React render errors so we created a Jest setup file that injects the DOM API into globals in every test. If you were using jsdom to do something similar in you tests, you can most likely remove your setup code and rely on the globals that kyt sets up. You can read about how to override the globals here](/docs/commands.md#test-globals).
Also, since Jest 20 updated the snapshot output, we had to regenerate some of our snapshots by running: npm run test -- -- -u
You can read more about new the new features that were released in Jest 19.0.2 -> 20.0.4.