  In some luminous supersoft X-ray sources (SSSs), hydrogen accretes onto the
surface of a white dwarf at rates more-or-less compatible with steady nuclear
burning. The white dwarfs in these systems therefore have a good chance to grow
in mass. Here we review what is known about the rate of Type Ia supernovae that
may be associated with SSSs. Observable consequences of the conjecture that
SSSs can be progenitors of Type Ia supernovae are also discussed.
