Objects with temperatures on the order of 30 eV and luminosities around 1038 erg/s have been established as a separate class by the recent ROSAT observations. The prototype supersoft x‐ray source (SSS) is the well‐known x‐ray binary CAL83 in the LMC, which has an orbital period of 1.04d. In the meantime about 10 SSS have been found in the Magellanic Clouds and at least 15 in the Andromeda Nebula. Two uncatalogued galactic supersoft sources have recently been discovered, but also the nova Muscae 1984 could be detected in a supersoft state 9 years after the explosion. In several cases dramatic time variability is found, with x‐ray on‐ and off‐states. The observations are summarized here. Several models have been suggested to explain the high luminosity and low temperature of SSS, all of them require very high mass accretion rates, which are also indicated in some of the optical spectra. In one interpretation the compact object is a neutron star (or black hole) shrouded by super‐Eddington accretion and the large radius and low temperature of the x‐ray photosphere is due to a Compton scattering cloud. If this were true, a large number of undetected supersoft neutron star binaries could help to moderate the millisecond pulsar birthrate problem. In the more likely interpretation, the compact object is a white dwarf burning nuclear fuel on its surface at the Eddington accretion rate. In this case the long‐sought predecessors for SN type‐Ia explosions might be among the class of supersoft sources.