Galaxy clusters are the most massive gravitationally collapsed structures in the universe, and they have important cosmological and astrophysical applications. 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 put these findings into context by comparing them to the results from dark matter simulations. 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. These mysterious galaxies have been found to be surprisingly abundant in local clusters, but their origin remains puzzling. I will discuss what we can learn about the properties of UDGs by studying their abundance as a function of halo mass, and their radial distribution in these haloes.