Neutron stars provide a window into the properties of dense nuclear matter. Several recent observational and theoretical developments provide powerful constraints on their structure and internal composition. Among these are the first observed binary neutron star merger, GW170817, whose gravitational radiation was accompanied by electromagnetic radiation from a short γ-ray burst and an optical afterglow believed to be due to the radioactive decay of newly minted heavy r-process nuclei. These observations give important constraints on the radii of typical neutron stars and on the upper limit to the neutron star maximum mass and complement recent pulsar observations that established a lower limit. Pulse-profile observations by the Neutron Star Interior Composition Explorer (NICER) X-ray telescope provide an independent, consistent measure of the neutron star radius. Theoretical many-body studies of neutron matter reinforce these estimates of neutron star radii. Studies using parameterized dense matter equations of state (EOSs) reveal several EOS-independent relations connecting global neutron star properties.