Reverse crunches work by forcing the lower abdominal muscles (primarily) to tense so as to control the descend of your legs. Paradoxically the abdominal muscles relax in the upswing of the legs so that you end up doing work when logically you should be resting (i.e. when the legs are going down) and resting when you would exepct to be working (i.e. when the legs are rising). 

What's involved: Abs, lower abs, front hip flexors. 

Powered by: Lower abs, front hip flexors. 

Tip: You can increase the pressure on your abs and make gains faster by raising your head and placing your chin on your chest so that you bring the upper abdominals into play.