Luminous supersoft X-ray sources were discovered with the Einstein obs
ervatory and have been established as an important new class of X-ray
binaries on the basis of observations with the Roentgen Satellite (ROS
AT). They have extremely soft spectra (equivalent blackbody temperatur
es of similar to 15-80 eV) and are highly luminous (bolometric luminos
ities of 10(36)-10(38) erg 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 10(3). Their observed characteristics are consis
tent with those of white dwarfs, which are steadily or cyclically burn
ing hydrogen-rich matter accreted onto the surface at a rate of order
10(-7) M-. year(-1). The required high accretion rates can be supplied
by mass transfer on a thermal time scale (10(6)-10(7) years) from clo
se companion stars that are more massive than the white dwarf accretor
, typically 1.3-2.5M(.). 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 ve
ry massive white dwarfs accreting at high rates. Luminous supersoft so
urces may make a considerable contribution to the Type Ia supernova ra
te in spiral and irregular galaxies.