In this talk I will present recent results concerning the level set formulation of the crystalline mean curvature flow. In a joint work with Yoshikazu Giga, we introduce a new notion of viscosity solutions for this problem and establish its well-posedness for compact crystals in an arbitrary dimension as well as the stability with respect to an approximation by a smooth anisotropic mean curvature flow. Since the crystalline mean curvature might not be defined even for smooth surfaces, we consider a restricted class of "faceted" test functions and show that it is sufficiently large to yield a general comparison principle.