I summarize what is know about the evolution of galaxies in clusters from the observational point of view presenting results at high (z~1), intermediate (z~0.5) and low (z~0) redshifts. I comment on the comparison between observations and predictions of CDM models, highlighting the observational landmarks more relevant for this comparison, such as the establishment and evolution of the morphology-density relation, the Butcher-Oemler effect, the evolution of red galaxies/ellipticals, the star formation histories of galaxies in clusters, the downsizing effect and the history of mass assembly.

16 pages - Available online at http://pos.sissa.it (Proceedings of Science) - eds. R.J. Dettmar, U. Klein, P. Salucci - Invited lecture at the Bochun/Bonn Graduate Research School ``Baryons in Dark Matter Halos'' (Novigrad, Oct 2004)