An open book for a contact 3-manifold is a pair (S, \phi), where S is an orientable surface with boundary, and \phi is a monodromy map which is the identity near the boundary of S. In recent work, John Baldwin investigated the effect "capping off" boundary components of S has on the Ozsvath-Szabo contact invariant. In this talk, I plan to give a survey of some of his results. In particular, I hope to show how his techniques can be used to prove the existence of contact structures which are only supported by open books of positive genus.