  The first inspiral of two neutron stars observed in gravitational waves was
remarkably close, allowing the kind of simultaneous gravitational wave and
electromagnetic observation that had not been expected for several years. Their
merger, followed by a gamma-ray burst and a kilonova, was observed across the
spectral bands of electromagnetic telescopes. These GW and electromagnetic
observations have led to dramatic advances in understanding short gamma-ray
bursts; determining the origin of the heaviest elements; and determining the
maximum mass of neutron stars. From the imprint of tides on the gravitational
waveforms and from observations of X-ray binaries, one can extract the radius
and deformability of inspiraling neutron stars. Together, the radius, maximum
mass, and causality constrain the neutron-star equation of state, and future
constraints can come from observations of post-merger oscillations. We
selectively review these results, filling in some of the physics with
derivations and estimates.
