This article presents a state space output regulation theory for linear infinite-dimensional systems (with bounded control, observation, and feedthrough operators) in which the reference and disturbance signals are bounded and uniformly continuous. Output regulation problems are posed and solved for both feedforward and error feedback controllers. Furthermore, under certain assumptions necessary conditions are obtained for those controllers which solve these output regulation problems. One consequence of these necessary conditions is a generalization of the well-known internal model principle. A key feature in our theory is that the exogenous system generating the reference and disturbance signals is infinite-dimensional.