We have developed several Krylov projection-based model-order reduction techniques to simulate electromagnetic wave propagation and diffusion in unbounded domains. Such techniques can be used to efficiently approximate transfer function field responses between a given set of sources and receivers and allow for fast and memory-efficient computation of Jacobians, thereby lowering the computational burden associated with inverse scattering problems. We found how general wavefield principles such as reciprocity, passivity, and the Schwarz reflection principle translate from the analytical to the numerical domain and developed polynomial, extended, and rational Krylov model-order reduction techniques that preserve these structures. Furthermore, we found that the symmetry of the Maxwell equations allows for projection onto polynomial and extended Krylov subspaces without saving a complete basis. In particular, short-term recurrence relations can be used to construct reduced-order models that are as memory efficient as time-stepping algorithms. In addition, we evaluated the differences between Krylov reduced-order methods for the full wave and diffusive Maxwell equations and we developed numerical examples to highlight the advantages and disadvantages of the discussed methods.