The Intergalactic Medium (IGM) is the principal reservoir of baryons produced in the Big Bang. Its structure and evolution have been elucidated within the context of a LCDM cosmology in great detail, with a precision second only to predictions for the Cosmic Microwave Background (CMB), but on much smaller scales. A review will be presented of the achievements in modelling the IGM, including the recent successes in providing evidence for a non-vanishing vacuum energy complementary to CMB and supernovae measurements. Illustrations will also be provided demonstrating how IGM science is now transitioning into a tool for constraining models of galaxy formation and the properties of Quasi-Stellar Objects.