  It has been predicted that quark and hybrid stars, containing strange quark
matter in their core, have a significantly smaller radius than ordinary neutron
stars. Preliminary X-ray observations of isolated neutron stars indicated a
surprisingly small radius consistent with quark matter in the interior of the
star. However, a new analysis of the data led to a radius corresponding to an
ordinary neutron star. In the present talk we will discuss theoretical
calculations of the mass-radius relation for quark and hybrid stars, taking
into account medium effects in quark matter, and report on recent X-ray
observations by Chandra and XMM and their latest interpretation.
