How massive can galaxies become within the standard ΛCDM cosmological model? We explore this question by studying the most massive galaxies expected at different cosmic epochs, using extreme value statistics to account for the finite volumes probed by observations. We examine how the galaxy stellar mass function, scatter in the stellar-to-halo mass relation, and observational uncertainties affect these predictions, and discuss what the most massive observed galaxies can tell us about galaxy formation in the early Universe.