I present a study on the impact of environment on galaxy evolution in distant galaxy clusters between redshifts 0.5 and 1.0. We find candidate galaxy clusters by applying a friends-of-friends algorithm to the deep photometric data of the UKIDSS Ultra-Deep Survey. Through studying the stellar mass functions, we reveal a strong excess of low-mass rapidly-quenched galaxies in cluster environments compared to the field. This indicates that low-mass objects are preferentially quenched in dense environments. I also show the radial distribution of different galaxy populations as a function of cluster-centric distance, which provides insight about where this environmental quenching is taking place and its timescale. Finally, I explain how these results, taken together, point to the existence of two environmental quenching pathways (fast and slow), operating on different timescales. Fast quenching acts on galaxies with high sSFR, switching them off on timescales shorter than the cluster dynamical time, and is more efficient for quenching low-mass galaxies. In contrast, slow quenching affects galaxies with moderate sSFR regardless of their stellar mass, acting on longer timescales.