After giving up on the 16 bit ceiling, Unicode briefly ballooned up to 31 bits (2 billion characters?) and then dropped down to 21 bits (a mere million or so characters, of which less that 120,000 are allocated so far).
The number 21 may seem odd, but really there was no reason any more to worry about byte boundaries (if there ever was) and 21 bits works out well with encoding schemes (such as the mighty UTF-8).
With 21 bits, there are then 17 planes of 64k each, of which the original BMP is just one, and the rest are "Supplemental", sometimes called "Astral Planes" (a joke which I sincerely hope translates better than "Han Unification").
Only two of the Astral Planes have any codepoints allocated, and the two highest ones are "private use": the Unicode Consortium promises not to touch them.