Studies of black holes are at a threshold. There is compelling evidence for the existence of both stellar-mass and supermassive black holes, and research is now focused on determining their properties and environmental effects. Most importantly, we are starting to realize the long-held promise of black holes as the ultimate laboratories for studying gravity in the strong-field limit. X-ray observations are already providing probes of the strong-gravity region around black holes, including evidence for the effects of black hole spin. However, a dramatic increase in collecting area and spectral resolution is required if we are to fully realize the potential of broad iron lines as probes of the strong-gravity region around black holes. Here, we will describe how the IXO will allow detailed studies of relativistic accretion, open the observational window on the astrophysics of black hole spin, and provide the first X-ray tests of strong-field General Relativity.