The cerebellum – sometimes known as the "little brain" – is located underneath the two hemispheres. It looks different from the rest of the brain because it consists of much smaller and more compact folds of tissue. It represents about 10 per cent of the brain's total volume but contains 50 per cent of its neurons.
This is an insane and fascinating finding. The cerebellum is a mystery to pretty much everyone, I think. I've been reading about and professionally studying the brain for close to a decade, and I can say with full confidence that I have very little idea what it does. People always say it has roles in this or that, without really articulating what it does--probably because they don't know either.
Quite a few, actually. The brain is pretty much the most complex system that we've ever encountered. There is so much about it that we don't yet understand. Take acupuncture, for example. (N.B. I'm speaking from memory here, so this might be wrong - can't find where I originally read it atm) It seems like BS pseudoscience, but research has demonstrated that stimulating acupuncture points that are supposed to be connected to other parts of the body actually results in neural activity in regions very similar to those that movement of the connected body parts lights up.