AbstractCell fate decisions are controlled by complex intracellular molecular regulatory networks. Studies increasingly reveal the scale of this complexity: not only do cell fate regulatory networks contain numerous positive and negative feedback loops, they also involve a range of different kinds of nonlinear protein–protein and protein–DNA interactions. This inherent complexity and nonlinearity makes cell fate decisions hard to understand using experiment and intuition alone. In this primer, we will outline how tools from mathematics can be used to understand cell fate dynamics. We will briefly introduce some notions from dynamical systems theory, and discuss how they offer a framework within which to build a rigorous understanding of what we mean by a cell “fate”, and how cells change fate. We will also outline how modern experiments, particularly high‐throughput single‐cell experiments, are enabling us to test and explore the limits of these ideas, and build a better understanding of cellular identities.This article is categorized under: Models of Systems Properties and Processes > Mechanistic Models Biological Mechanisms > Cell Fates Models of Systems Properties and Processes > Cellular Models