Time-domain solutions of Maxwell’s equations provide information on wave interactions involving multiple frequencies and can describe nonlinear phenomena such as second harmonic generation and parametric amplification in nonlinear optical materials. In this chapter, we will discuss two time-domain numerical methods for solving transient Maxwell’s equations. The first one is a high-order discontinuous Galerkin (DG) method on unstructured finite element meshes. High-order hierarchical basis functions for the DG discretization will be presented. The second is the popular finite difference Yee scheme on staggered Cartesian grids.