  I discuss constraints on the equation of state of matter at supra-nuclear
densities that can be derived from observations of neutron stars. I focus on
recent work on Vela X-1, which may well be substantially more massive than the
canonical 1.4 solar masses, and on the prospects offered by the `isolated' or
`thermally-emitting' neutron stars. I present a re-analysis of the LETG
observations of the brightest of the isolated neutron stars, RX J1856.5-3754,
and find that the spectrum shows, unlike all other neutron stars observed so
far, a significant absorption feature, near 39 Angstrom.
