One of the outstanding challenges in atomistic simulations of materials is how to reach physically meaningful time scales. While the fundamental time scale of the atomistic models is that of the atomic vibration period of picoseconds, physically meaningful phenomenon may take microseconds or longer to occur. This precludes a direct numerical simulation with, for instance, a Langevin model of the material from reaching such physical time scales. The time scale separation challenge has motivated the development of a variety of multiscale methods, including accelerated molecular dynamics, kinetic Monte Carlo, phase field models, and diffusive molecular dynamics. In this talk, I will survey some of these approaches and discuss common mathematical assumptions that underly them while also highlighting where approximations have been made. Rigorous results will be presented, where available, along with outstanding mathematical challenges.