Pseudo-isotopy is an equivalence relation on homeomorphisms that lies between isotopy and homotopy. Classifying homeomorphisms of 4-manifolds up to pseudo-isotopy is a potentially tractable problem, whereas isotopy classifications currently elude us outside of the simply-connected case. I will explain a program to understand some of this difference using the smooth invariants of Hatcher-Wagoner and Igusa. A result is the construction of many examples of homeomorphisms that are pseudo-isotopic to the identity but not isotopic to the identity on a range of 4-manifolds, including the 4-torus. This is joint work with Isacco Nonino.