We discuss computational methods for solving stochastic differential equations. Monte Carlo computations typically average some quantity of interest over many approximate sample paths of the SDE. We review the convergence theory for SDE time stepping methods in the weak and pathwise senses. We offer an alternative to these that studies the accuracy of the joint distribution of approximate paths at the discrete time steps. The convergence analysis in this sense centers on short time asymptotic approximations to the advection diffusion equation that governs the transition probability density for paths over a time step. The expansion in Gaussians and Hermite polynomials is not new, but we need new L^1 error estimates. This is joint work with Peter Glynn, Jose Antonio Peres, and Sangmin Lee.