Radio galaxies and quasars are the most powerful and spectacular objects in the Universe. They are therefore of immense interest in their own right, and provide unique physical laboratories for the study of extremes in physics such as highly-relativistic motion and relativistic gravity. However, as I hope to convince you, these most luminous of astronomical sources are also of more general interest for understanding the formation and evolution of the Universe of 'normal' galaxies. In this article, I first relate how these phenomenal 'cosmic fireworks' were discovered, and summarize their somewhat amazing properties. I then explain how 50 years of increasingly sophisticated observations coupled with the application of standard physics has led to our current 'unified model' of how these sources 'work'. Next I describe current observational efforts to identify precisely how these sources are triggered into action, and how such fuelling mechanisms might relate to the fact that radio galaxies and quasars were much more numerous in the young universe than they are today. Finally, I explain how these high-energy objects can be used as cosmic beacons to locate very distant galaxies and hence enable the formation and evolution of galaxies of stars to be studied back to within 1 billion years of the Big Bang, and how the cosmological evolution of radio galaxies and quasars may be closely related to the overall star-formation history of our Universe. I conclude with a brief overview of the exciting prospects for future improvements in our understanding of these sources and their evolution, through the use of new observational facilities such as the Space Telescope and the new generation of large groundbased telescopes.