Yuval Wigderson of ETH Zürich gives this Institute for Advanced Study Discrete Mathematics Seminar on the regularity lemma, the result stating that any discrete object can be partitioned into a bounded number of pseudorandom pieces. He asks how small that bound can be made, and whether assuming the object is combinatorially simple lets the bound shrink further. The talk works through several variants and generalizations of VC dimension, the classical measure of a set system's complexity from statistical learning theory, showing how these notions become the tool for pinning down regularity bounds for simple structures. The material is based on joint work with Lior Gishboliner and Asaf Shapira. Delivered at a chalk-and-slides research level for an audience already familiar with extremal and additive combinatorics, the talk moves from definitions through open questions to recent theorems connecting VC dimension and regularity partitions.