High resolution Chandra X-ray observations show the importance of the X-ray band for studying the evolution of galaxies. Binary X-ray sources are an easily detectable tracer of the stellar population. Chandra studies of these populations are giving us insights on the nature and formation of these binaries, and provide the basis for diagnostics of galaxy evolution. With Chandra and XMM we can explore relatively poorly known aspects of the black hole population of the universe. One example are ultra-luminous X-ray sources, that may be connected with the `missing' intermediate mass black holes predicted by hierarchical galaxy and black hole formation scenarios. Another example is the study of quiescent supermassive nuclear black holes and their surroundings, as a way to understand the full range of the AGN phenomenon. Finally, the X-ray band provides the only way to explore hot plasmas in galaxies; Chandra and XMM observations are revealing the importance of these plasmas as vehicles of both chemical enrichment and energy.