Violent activity in the nuclei of galaxies has long been considered a curiosity in its own right; manifestations of this phenomenon include distant quasars in the early Universe and comparatively nearby Seyfert galaxies, both thought to be powered by the release of gravitational potential energy as material from the host galaxy accretes onto a central supermassive black hole (SMBH). Traditionally, the broader study of the formation, structure and evolution of galaxies has largely excluded active galactic nuclei. Recently, however, this situation has changed dramatically, both observationally and theoretically, with the realization that the growth and influence of the SMBH, the origin and development of galaxies and nuclear activity at different epochs in the Universe may be intimately related. The most spectacular fireworks seen in distant quasars may be relatively easy to explain, since the era of greatest quasar activity seems to coincide with turbulent dynamics at the epoch of galaxy formation in the young, gas-rich Universe. Ubiquitous black holes are believed to be a legacy of this violent birth. Alternatively, black holes may be the seeds that drive galaxy formation in the first place. Closer to home, and hence more recently in the history of the Universe, a fraction of comparatively ordinary galaxies, similar to our own, has reignited their central engines, albeit at a lower level of activity. Since these galaxies are more established than their younger and more distant counterparts, the activity here is all the more puzzling. Whatever the mechanisms involved, they are likely to play an important role in galaxy evolution. I review the intriguing evidence for causal links between SMBHs, nuclear activity and the formation and evolution of galaxies, and describe opportunities for testing these relationships using the next generation of earthbound and space-borne astronomical facilities.