Measurement of Neutron Star Radii with X-ray Binaries and Recycled Pulsars

Detailed modeling of the observed surface X-ray radiation from neutron stars can in principle reveal their interior structure, thereby constraining the state of matter at the most extreme densities. This talk will provide a summary of on-going observational efforts with the \textit{Chandra X-ray Observatory} and \textit{XMM-Newton} towards this end, with a focus on two particular varieties of neutron stars -- thermally-emitting quiescent low-mass X-ray binaries and ``recycled'' millisecond pulsars. An overview of future prospects for measuring the elusive neutron star equation of state using forthcoming X-ray missions such as the Neutron Star Interior Composition ExploreR (NICER) and Athena+ will also be presented.