Microsoft's messaging app Skype looks like it's getting another friendly face in an upcoming version -- yours! A split-screen feature for displaying what's happening on your side of the call appeared in a beta build of the app (the Skype Insider program), so you'll likely see it in an upcoming release.
Screen sharing can be used for showing documents without having to send them before discussing: not as fun as collaboratively shopping for clothes, movie viewing or mocking a series of texts from your mom, which you can also do, but more practical.
And you can record the sessions, but the app will record any notifications that pop up as well. So share carefully!