The goal of this work is to create a framework that (1) provides applied researchers with a set of practical tools and (2) clearly lays out all the relevant assumptions for assessing treatment effect variation. We build this from the ground up, laying out a randomization-based framework for characterizing and understanding treatment effect heterogeneity in a range of settings, including observational studies. Following a long tradition in statistics, we use potential outcomes (Rubin, 1974; Neyman, 1923 [1990]) as the building blocks of this framework, allowing us to clearly separate the quantities of interest from the estimation methods. We decompose overall treatment effect heterogeneity into two components, the systematic component, impact variation explained by covariates, and the idiosyncratic component, impact variation not explained by covariates. (author abstract)