Homogenization is the approximation of a complex, “disordered” system by a simpler, “ordered” one. Picture a walker on a grid. In each step, the walker chooses to walk along a neighboring edge with equal probability. At large scales, the walker approximates Brownian motion. But what if some edges are more likely to be traversed than others? I will discuss recent advances in the theory of quantitative homogenization which make it possible to analyze random walk with drift and other models in probability. Joint work with Scott Armstrong and Tuomo Kuusi.