Many problems in mathematical physics involve disorder across various length scales, and a central question is to predict (or estimate the size of) critical length scales beyond which disorder can be integrated out. This is often addressed heuristically using renormalization group arguments. In this lecture, we will present a rigorous approach to this problem in the context of homogenization of diffusion equations. We consider equations which exhibit a very large ellipticity contrast ratio, and are interested in the length scale at which we see homogenization (with high probability). We introduce a coarse-graining scheme, allowing us to integrate out the disorder scale-by-scale, which can be seen as a rigorous renormalization group argument. Our techniques may be iterated across many scales, allowing us to treat random fields with multifractal structure (leading in some cases to anomalous diffusion). This is joint work with Tuomo Kuusi.