I will present a study of galaxy populations in distant galaxy clusters, focussing in particular on post-starburst galaxies as probes of the likely quenching processes. I will first introduce the method I have developed and optimised for the detection of galaxy clusters within deep photometric surveys, and apply this method to the 0.8 deg^2 UDS survey. By comparing the mass functions of cluster and field galaxies in the redshift range from 0.5 to 1.0, I will show that galaxy populations at this epoch are significantly affected by their environment. Low-mass galaxies in particular are seen to be preferentially quenched in dense environments, as shown by a clear excess of low-mass passive and post-starburst galaxies. The radial distributions of these galaxies shed further light on the quenching processes. While post-starburst galaxies have very similar mass functions to young star-forming galaxies, their radial distributions are very different, and more consistent with the quiescent population. Our results suggest that star-forming galaxies are quenched as they enter the dense inner regions of clusters. I will conclude by proposing a model involving two possible environmentally-driven quenching pathways: rapid quenching of low-mass (perhaps by merging or ram-pressure stripping), and slow quenching, triggered by a more gentle gas removal, leading to the strangulation of the galaxies.