Over the next decade or so, the gravitational-wave window onto the Universe will be opened in four frequency bands that span 22 orders of magnitude: The high-frequency band, 10 to 10,000 Hz (ground-based interferometers such as LIGO and VIRGO), the low-frequency band, 10-5 to 0.1 Hz (the space-based interferometer LISA), the very-low frequency band, 10-9 to 10-7 Hz (pulsar timing arrays), and the extremely-low-frequency band, 10-18 to 10-16 Hz (polarization of the cosmic microwave background). This lecture will describe these four bands, the detectors that are being developed to explore them, and what we are likely to learn about black holes, neutron stars, white dwarfs and early-universe exotica from these detectors' observations.