2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/3540I 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.10 pages, 3 figures, uses newpasp.sty (included). To appear in Proc. Jan van Paradijs Memorial Symposium, ed. Van den Heuvel, E. P. J., Kaper, L., Rol, E. (ASP, San Fransisco)Astrophysicstext