We have developed a fluid-mechanical model of a eucaryotic axoneme that couples the internal force generation of dynein molecular motors, the passive elastic mechanics of microtubules, and forces due to nexin links with a surrounding incompressible fluid. This model has been used to examine both ciliary beating and flagellar motility. In this article, we show preliminary simulation results for sperm motility in both viscous and viscoelastic fluids, as well as multiciliary interaction with a mucus layer.