Recent developments have ushered in a new era in the field of black hole astrophysics, providing our first direct view of the remarkable environment near black hole event horizons. These observations have enabled astronomers to confirm long-standing ideas on the physics of gas flowing into black holes with temperatures that are hundreds of times greater than at the center of the Sun. In this talk I will describe the successes and challenges of theoretical models of black hole accretion on event horizon scales in the context of these observational advances. I will conclude with ideas on how the interplay of theory and observations can be used to measure the spin of black holes and test the long-standing prediction that the rotational energy of black holes can be extracted to power astrophysical jets.