Our present view of the universe is dominated by electromagnetic radiation --- radio, infrared, visible light, x-rays, gamma rays. Other forms of radiation bathe us every moment, but are not so easy to sense. Measuring them can nonetheless tell us quite a lot about our universe. In this talk, I will describe gravitational waves, ripples of spacetime predicted by Einstein's 1915 reformulation of gravity. These waves arise from rapid motions of very dense objects, like neutron stars and black holes.  I will show how to measure these waves, describing observations which demonstrate that certain binary star systems emit strong gravitational waves, as well as our present efforts to build antennae which will routinely measure these waves directly.  Finally, I will describe the payoff of these measurements. Gravitational waves can give us an extraordinary view of violent astrophysical phenomena, opening new ways to map and understand some of the most energetic events in the universe.  Their ability to teach us about massive black holes is particularly promising, and will be a focus of the examples I describe in this talk.