We review the properties and behavior of 20 X-ray binaries that contain a dynamically-confirmed black hole, 17 of which are transient systems. During the past decade, many of these transient sources were observed daily throughout the course of their typically year-long outburst cycles using the large-area timing detector aboard theRossi X-Ray Timing Explorer. The evolution of these transient sources is complex. Nevertheless, there are behavior patterns common to all of them as we show in a comprehensive comparison of six selected systems. Central to this comparison are three X-ray states of accretion, which are reviewed and defined quantitatively. We discuss phenomena that arise in strong gravitational fields, including relativistically-broadened Fe lines, high-frequency quasi-periodic oscillations (100–450 Hz), and relativistic radio and X-ray jets. Such phenomena show us how a black hole interacts with its environment, thereby complementing the picture of black holes that gravitational wave detectors will provide. We sketch a scenario for the potential impact of timing/spectral studies of accreting black holes on physics and discuss a current frontier topic, namely, the measurement of black hole spin.