In this talk, I will give an introduction to the direct numerical approximation of Maxwell's equations, with emphasis on finite difference and finite element methods in the time domain. In 1966 Kane Yee from Lawrence Livermore National Laboratory proposed a finite difference scheme for the time-domain Maxwell's equations which is now well known as the Finite Difference Time Domain (FDTD) or Yee scheme. The FDTD scheme has become a standard in computational electromagnetics. In the 1980's J.C. Nedelec popularized a family of mixed finite elements called edge elements for the numerical simulation of Maxwell's equations. Thereafter many different finite elements methods, as well as finite volume and finite difference methods, have been constructed. On structured, Cartesian grids many of these schemes share similarities to the original Yee FDTD scheme. I will talk about the numerical aspects of these methods including their stability, dispersion and accuracy properties. The talk is aimed at graduate students who have a background in numerical analysis of partial differential equations.