Measurements of the radial distribution of galaxies in clusters show how galaxies trace the underlying dark matter distribution, and provide constraints on the physics related to their evolution in these environments. I will present measurements on the radial distribution of galaxies in two cluster samples, which span about 8 Gyrs of lookback time. By matching local galaxy clusters to their progenitors at high redshift, we study how clusters assemble their stellar mass content. Interestingly, this suggests that the central part of the stellar mass distribution of local galaxy clusters is already in place at redshift, and any further growth seems to happen in an inside-out fashion. I will also focus on the abundance and spatial distribution of ultra-diffuse galaxies (UDGs, which have the luminosities of dwarfs but sizes of giant galaxies) in clusters and groups. These mysterious galaxies have been found to be surprisingly abundant in local clusters, but their origin remains puzzling. I will summarise recent results on their abundance as a function of host halo mass, and the first direct measurement of their masses using weak gravitational lensing. I will discuss implications and future prospects to learn more about the properties and formation histories of these elusive galaxies.