Over the last two years, the Advanced LIGO and Advanced Virgo detectors have observed a handful of gravitational-wave events from the inspiral and merger of binary black holes in distant galaxies. These events have resulted in the first measurements of the fundamental properties of gravitational waves, tests of General Relativity in the strong-field, highly-dynamical regime, and the population, masses and spins of black holes in the universe. Most recently, signals were detected from the inspiral of a binary neutron star system, GW170817. That event is thus far the loudest (highest signal-to-noise ratio) and closest gravitational-wave event observed. A gamma-ray burst detected 1.7 seconds after merger confirms the long-held hypothesis that BNS mergers are associated with short gamma-ray bursts. The LIGO and Virgo data produced a three-dimensional sky localization of the source, enabling a successful electromagnetic follow-up campaign that identified an associated electromagnetic transient in a galaxy ~40 Mpc from Earth. A multi-messenger view of GW170817 from ~100 seconds before merger through weeks afterward provides evidence of a "kilonova", and of the production of heavy elements. For the first time, using gravitational waves we are able to constrain the equation of state of dense neutron stars and infer the rate of local binary neutron star mergers. When we include EM observations, we are able to directly measure the speed of gravitational waves, constrain its polarization content, independently measure the Hubble constant, probe the validity of the equivalence principle, and gain new insight into the astrophysical engine driving these events.