The presentations of this NATO Advanced Study Institute centre around X-ray clusters of galaxies and their role in understanding the structure and evolution of the universe. Reminiscences of the beginning of the extra-solar X-ray astronomy some 30 years ago, of subsequent X-ray satellites which, among other discoveries, found galaxy clusters to be an important new class of intrinsically bright X-ray sources, and highlights from the most recent All Sky Survey by ROSAT serve as an introduction.