A writer for the Washington Post reviews app Sleep Cycle. (It didn’t go well.)
The app is supposed to wake you during your lightest sleep phase within 30 minutes of the time set on your alarm; i.e., if your alarm is set for 7 a.m., it should wake you anytime between 6:30 and 7. That sounds like a solid theory, but Sleep Cycle never woke me up before my set alarm time — it apparently never thought I was ready.
Once awakened, either by your own music or one of the app’s soothing sounds, you are asked to record how you feel, using smiley/frowny faces. I hit a happy face only once, and then it was more or less as an ironic gesture.