Alright, my 2 cents...
I use only three variations of the crescent kick.
Front leg inside-to-outside crescent kick: I do this from a side or back stance. I add a very short, quick step or shuffle forward to generate more power. The part of the foot that connects with the target is either the side-blade, or the heel (with the foot only turned slightly). I never throw this just as a stand alone technique.
Many people throw this kick out way to wide, which makes it easy to see. I good set-up is to throw a front leg front kick a couple times (aimed low, toward the waist). Really get your opponent used to seeing that front leg performing a front kick. Program them to drop their guard. Once programmed, follow again with the crescent. The way I use and teach it, it starts out looking just like that front kick. This has a very good chance of dropping the opponents hands down, and the crescent then comes up and connects with the face.
The other use for this particular kick is as a sweep, a quick groin strike (when opponent is in a side stance), or a leg-check (using the downward heel motion, similar to an axe).
Spinning Crescent: I do this from a side stance or fighting stance. I generally only use this when I have an opponent that is in a side stance, holding their guard high, and might be moving around me as I come forward. I always throw it mid level, aimed for the stomach).
Jump Spinning Crescent: This kick has a suprising close range to it, which I guess is its strength. I could be standing close enough to touch my opponents head with my hand. I use this very little, like any jump spin kick. Target is either the head or stomach.
When sparring with my friend many years ago, I came in hard, and then backed-up and did the jump spin... I threw it more for fun, figuring he would still be far away. He followed me right away and walked right into the kick and got knocked down and dazed (wobbly legs).
Just like with any kick, each has a time and place. None of these are kicks are ones I deploy with any regularity, but they do have uses.