The last few years have seen new opportunities for
constraining the physics of neutron star interiors. I will first discuss the
current state of neutron star radius measurements and then go on to discuss
thermal tomography as a probe of the nuclear, magnetic, and transport
properties of neutron star crusts. In each case, I will emphasize the
astrophysics that must be understood to make reliable inferences about the
properties of dense matter from observations of neutron stars.