Many if not all big galaxies harbour supermassive black holes. Only a small fraction of these is currently active, appearing as Active Galactic Nuclei or quasars. But probably all big galaxies harboured a quasar-like nucleus at least once in their lives, if only for a relatively brief period. During and after those episodes, galaxy evolution may be severely affected through radiative and mechanical feedback from the actice nuclei. Of particular interest are therefore the morphological properties and colours of quasar host galaxies in comparison to `normal’ galaxies with no AGN. I present and discuss several observational experiments using the Hubble Space Telescope and other facilities. These results indicate that quasar hosts are most likely caught in transient phases of their evolution, evolving rapidly towards becoming red and dull spheroids. I also briefly discuss the prospects of identifying the actual feedback mechanism which so far has essentially been postulated rather than established.