  I review attempts made to determine the properties of neutron stars. I focus
on constraints on the maximum mass that a neutron star can have, and on
attempts to measure neutron-star radii. So far, there appears to be only one
neutron star for which there is strong evidence that its mass is above the
canonical 1.4 Msun, viz., Vela X-1, for which a mass close to 1.9 Msun is
found. Prospects for progress appear brightest for studies of systems in which
the neutron star should have accreted substantial amounts of matter. While for
individual systems the evidence that neutron stars can have high masses is
weak, the ensemble appears to show that masses around 1.6 Msun are possible.
For the radius determination, most attempts have focussed on neutron stars in
low-mass X-ray binaries in which accretion has temporarily shut down. These
neutron stars are easiest to model, since they should have pure Hydrogen
atmospheres and low magnetic fields. To obtain accurate radii, however,
requires precise distances and very high quality data.
