I review attempts made to determine the properties of neutron stars. The focus is on the maximum mass that a neutron star can have, or, conversely, the minimum mass required for the formation of a black hole. There appears to be only one neutron star for which there is strong evidence that its mass is above the canonical 1.4 solar masses, viz., Vela X-1, for which a mass close to 1.9 solar masses is found. Prospects for progress appear brightest for studies of systems in which the neutron star should have accreted substantial amounts of matter.Comment: 6 pages, 3 figures, to appear in Proc. ESO Workshop on "Black Holes in Binaries and Galactic Nuclei", Garching (Sept. 1999), L. Kaper, E.P.J. van den Heuvel, P.A. Woudt eds., Springer-Verla