Luminous supersoft X-ray sources were discovered with the Einstein observatory and have been established as an important new class of X-ray binaries on the basis of observations with the Roentgen Satellite (ROSAT). They have extremely soft spectra (equivalent blackbody temperatures of ∼15–80 eV) and are highly luminous (bolometric luminosities of 1036–1038erg s−1). Correcting for the heavy extinction of soft X rays by interstellar neutral hydrogen, their numbers in the disks of ordinary spiral galaxies like our own and M31 are estimated to be of the order of 103. Their observed characteristics are consistent with those of white dwarfs, which are steadily or cyclically burning hydrogen-rich matter accreted onto the surface at a rate of order 10−7[Formula: see text] year−1. The required high accretion rates can be supplied by mass transfer on a thermal time scale (106–107years) from close companion stars that are more massive than the white dwarf accretor, typically 1.3–2.5 [Formula: see text]. Steady burning can also occur in a post-nova stage, but for shorter time scales, and it has been observed in a few classical novae and symbiotic novae. A few supersoft sources have been found to be recurrent transients. They are possibly connected with very massive white dwarfs accreting at high rates. Luminous supersoft sources may make a considerable contribution to the Type Ia supernova rate in spiral and irregular galaxies.