Motion by (weighted) mean curvature is a geometric evolution law for surfaces, representing steepest descent with respect to (anisotropic) surface energy. The crystalline algorithm is a numerical method for computing this motion. The main idea of this method is to solve the analogous evolution law for a crystalline surface energy which approximates the underlying smooth one. We have recently explored the nature of this method, demonstrating its convergence in some simple special cases. This paper summarizes our results.