  Ever since the discovery of neutron stars it has been realized that they
serve as probes of a physical regime that cannot be accessed in laboratories:
strongly degenerate matter at several times nuclear saturation density.
Existing nuclear theories diverge widely in their predictions about such
matter. It could be that the matter is primarily nucleons, but it is also
possible that exotic species such as hyperons, free quarks, condensates, or
strange matter may dominate this regime. Astronomical observations of cold
high-density matter are necessarily indirect, which means that we must rely on
measurements of quantities such as the masses and radii of neutron stars and
their surface effective temperatures as a function of age. Here we review the
current status of constraints from various methods and the prospects for future
improvements.
