The structure of neutron stars, for example their radii and moments of inertia, depend on the symmetry properties of the nuclear interaction in the vicinity of the nuclear saturation density. Thus, limits to symmetry properties from nuclear measurements and theoretical neutron matter calculations provide very important constraints on neutron
stars and dense matter. New precision measurements of high-mass neutron stars, coupled with general relativity, enhance these constraints. Although measurements of neutron star radii through astronomical observations are not yet precise enough, anticipated measurements of thermal emission using the Neutron Star Interior Composition ExploreR (NICER), moments of inertia from pulsar timing observations, gravitational waves from neutron star mergers, and supernova neutrinos all have the potential of testing and refining these predictions.