We systematically analyzed about a terabyte of data from Galactic binary systems to characterize how these spectra change as a function of mass accretion rate. With this volume of data we are able to identify the differences in behaviour of black holes and neutron stars, implying that black holes really do have an event horizon. The spectral evolution seen as a function of L/LEdd can be linked to current state-of-the-art numerical simulations of accretion flows, and we develop qualitative and quantitative models of the spectral changes in all types of binary systems. The key ingredient of this picture is that the major hard-soft spectral transition is driven by a changing inner radius of the accretion disc. This also qualitatively explains the changes seen in the variability power spectra of these objects. This lays the foundation for a self-consistent, theoretically motivated framework in which to explain both the spectral and timing properties of accreting compact objects.