In recent years there have been a number of substantial advances in numerical techniques for solving the wave equation and Maxwell's equations in the time domain. These include: (i) Efficient methods for truncating unbounded domains which can provide arbitrary accuracy at low cost; (ii) Fast methods for evaluating the standard integral solution formulas, akin to the fast multipole method in the frequency domain; (iii) Discretization strategies focusing on techniques for using high order/high resolution approximations in complex geometry. I will review these new developments and discuss ideas for their improvement and extension to other wave propagation problems.