Abstract: In this talk I will address a few topics related to the brightest cluster galaxies (BCGs) and galaxy population in galaxy clusters. I will first review an age-old question, namely, are BCGs special, with respect to other luminous, red galaxies in clusters? I will then describe two novel approaches in studying the mass assembly history of BCGs, by connecting BCGs observed at different redshifts through the mass growth history of host clusters. Contrasting our results to the predictions of leading galaxy formation models suggests some discrepancy at z<0.5. Finally I will discuss the results from a study of the redshift evolution of the main baryonic components in clusters, i.e. hot intracluster medium (ICM) and galaxies, and note the curious conclusion that while the ICM follows the self-similar expectation, the stellar mass contained in galaxies does not appear to evolve up to z~0.6.