This unique volume provides a comprehensive survey of our understanding of the Universe based on the exact solutions of the theory of relativity. More precisely, it describes those models that fit with astronomical observations of galaxy clusters, cosmic voids and other key features of our Universe. This authoritative account achieves two important goals. Firstly, it collects together all independently derived cosmological solutions since the birth of relativity in 1915 to the present day, and clearly shows how they are interrelated. Secondly, it presents a coherent overview of the physical properties of these inhomogeneous models. It demonstrates, for instance, that the formation of voids and the interaction of the cosmic microwave background radiation with matter in the Universe can be explained by exact solutions of the Einstein equations, without the need for approximations. This book will be of particular interest to graduates and researchers in gravity, relativity and theoretical cosmology as well as historians of science.