The beating of a cilium is an elegant example of an actuated elastic structure coupled to a surrounding fluid. Computational fluid dynamics enthusiasts will recognize that ciliary systems present many complications such as the interaction of groups of cilia, the influence of boundaries, and the coupling to fluids that have complex rheology and microstructures. Moreover, the ciliary beatform is an emergent feature of these mechanical considerations along with biochemical processes. We will present an overview of current CFD models of cilia, along with some recent progress in analyzing fluid mixing by cilia and modeling ciliary penetration of a mucus layer.