Neutron Stars and Black Holes: New clues from Chandra and XMM-Newton

Neutron stars and black holes, the most compact astrophysical objects, have become observable in many different ways during the last few decades. We will first review the phenomenology and properties of neutron stars and black holes (stellar and supermassive) as derived from multiwavelength observatories. Recently much progress has been made by means of the new powerful X-ray observatories Chandra and XMM-Newton which provide a substantial increase in sensitivity as well as spectral and angular resolution compared with previous satellites like ROSAT and ASCA. We shall discuss in more detail two recent topics: (1) The attempts to use X-ray spectroscopy for measuring the radii of neutron stars which depend on the equation of state at supranuclear densities. Have quark stars been detected? (2) The diagnostics of the strong gravity regions around supermassive black holes using X-ray spectroscopy.