A survey of regularity results for finite energy solutions to initial-boundary value problems for hyperbolic operators of second-order is given. After discussing Dirichlet boundary conditions where the theory is fairly straightforward, the talk will center on Neumann boundary conditions. Results proved by Miyatake (1973) , Lasiecka and Triggiani (1990), and Tataru (1998) will be presented. We will close with some related estimates on traces of eigenfunctions for the Neumann Laplacian which have been established more recently by Hassell and Tao (2002/2010), and Barnett, Hassell, and Tacy (2018). Time permitting some regularity theory for symmetric hyperbolic systems will be discussed.