In this talk, we will describe a multiscale analysis for decomposing high-dimensional measures into simpler structures. The strategy is based on the renormalization group method used in statistical physics to study the distribution of interacting particle systems. We will first apply this framework to Gibbs measures, showing how it can be used to derive functional inequalities. We will also discuss how this decomposition can be understood from the perspective of transport of measures, and survey other related developments, including numerical methods for sampling from high-dimensional probability distributions.