What are compact cranks? In overheard in a post ride discussion this morning about wanting a set of compact cranks.
My search on bicycles.se has only found this question with them in the title, but the answers don't mention exactly what they are.  

Are they similar to the old biopace cranks?
They probably weren't talking about the cranks per-se, but the whole crankset, which is the cranks and the chainrings. 

Compacts are cranksets with smaller chainrings (typically 50 teeth and 34 teeth) as opposed to standard cranksets which have say 52:42. Combined with wide-range cassette this can give a good range of gears without having to have a triple-ring.  

Biopace were oval rings - you can get non-round chainrings for either compact or regular cranksets.

Note that the cranks themselves do come in different lengths to account for different leg-lengths, but this is independent of the chainring diameter.