This volume contains nine survey articles based on plenary lectures given at the 28th British Combinatorial Conference, hosted online by Durham University in July 2021.This biennial conference is a well-established international event, attracting speakers from around the world.Written by some of the foremost researchers in the field, these surveys provide up-to-date overviews of several areas of contemporary interest in combinatorics.Topics discussed include maximal subgroups of finite simple groups, Hasse–Weil type theorems and relevant classes of polynomial functions, the partition complex, the graph isomorphism problem, and Borel combinatorics.Representing a snapshot of current developments in combinatorics, this book will be of interest to researchers and graduate students in mathematics and theoretical computer science.