We summarize our current knowledge of neutron star masses and radii. Recent instrumentation and computational advances have resulted in a rapid increase in the discovery rate and precise timing of radio pulsars in binaries in the last few years, leading to a large number of mass measurements. These discoveries show that the neutron star mass distribution is much wider than previously thought, with 3 known pulsars now firmly in the 1.9−2.0 M⊙ mass range. For radii, large, high quality datasets from X-ray satellites as well as significant progress in theoretical modeling led to considerable progress in the measurements, placing them in the 9.9 − 11.2 km range and shrinking their uncertainties due to a better understanding of the sources of systematic errors. The combination of the massive neutron star discoveries, the tighter radius measurements, and improved laboratory constraints of the properties of dense matter has already made a substantial impact on our understanding of the composition and bulk properties of cold nuclear matter at densities higher than that of the atomic nucleus, a major unsolved problem in modern physics.