We give an introduction to descriptive combinatorics: the study of "definable" graphs, colorings, set families, etc. on nice topological spaces such as the reals. We then present one concrete result in this area, showing that every definable graph whose components are "approximately tree-like" may be turned into a genuine forest with the same components in a definable manner. This is joint work with Antoine Poulin, Ran Tao, and Anush Tserunyan.