How *do* cats land on their feet when falling, anyway?

So what intrigued and, quite frankly, baffled physicists for so long? The surprising observation is that cats can still turn over in free-fall even when they are released at rest, i.e. with no initial rotation! Ironically, this probably freaks out physicists far more than non-physicists, because at first glance it appears to be a violation of the conservation of angular momentum.