I will briefly discuss the separate computational challenges posed by anisotropy & inhomogeneity in front propagation and optimal control problems. The idea of "homogenization" will be introduced informally as a practical approach for dealing with some of these challenges. I will then describe the key results (from a joint work with A. Oberman and R. Takei) on 2-scale and 3-scale computations in geometric optics. We propose a new & efficient method to homogenize first-order Hamilton-Jacobi PDEs. Unlike the prior cell-problem methods, our algorithm is based on homogenization of the related Finsler metric. We illustrate by computing the effective velocity profiles for a number of periodic and random composite materials.