A central question in arithmetic statistics is to understand the distribution of class groups across families of global fields. This line of inquiry began with the conjectures of Cohen and Lenstra, which predict the distribution of the odd part of class group of quadratic fields. Over the past two decades, significant progress has been made in various directions, including the proof of function field analogues of the Cohen–Lenstra heuristics, the study of nonabelian generalizations of class groups, and the exploration of how these distributions vary across different families of global fields. In this talk, I will survey the history and recent developments of the (nonabelian) Cohen–Lenstra heuristics.