Dilute ultracold quantum gases have been of intense interest for the past decade. Bosonic gases condense to become superfluids, analogous to superfluid helium, but considerably simpler and therefore amenable to theoretical analysis. Fermionic gases become superfluids through a pairing mechanism analogous to conventional metallic superconductors. Both of these systems serve as laboratories for the study of quantum superfluids under various extreme or unusual conditions such as fast rotation or confinement in optical lattices. Current problems of interest are the structure and arrangement of quantized vortices in rapidly rotating Bose-Einstein condensates.