We are seeking both electromagnetic and gravitational waves from binary supermassive black holes, the biggest, discrete binary systems in the Universe. When galaxies merge, these giant binaries can form. During their inspiral and coalescence phases, they will produce intense gravitational radiation, which we expect to detect with gravitational-wave observatories like Pulsar Timing Arrays and LISA in the coming decade. Pulsar timing arrays use distributed networks of pulsars to sense these waves as they pass through our galaxy; in effect, they are an observatory on a Galactic scale. This talk will discuss the exciting latest results from pulsar timing arrays, including an interesting "noise signal" and what our latest, most stringent limits on gravitational waves mean for galaxy evolution and supermassive binary black holes. I will also briefly discuss efforts to discover both gravitational and electromagnetic waves from binary supermassive black holes.