I review some recent work (done in collaboration with G. Veneziano) which c
larifies the existence of a correspondence between self-gravitating fundame
ntal string states and Schwarzschild black holes. The main result is a deta
iled calculation showing that self gravity causes a typical string state of
mass M to shrink, as the string coupling g(2) increases, down to a compact
string state whose mass, size, entropy and luminosity match (for the criti
cal value g(c)(2) similar to (M root alpha')(-1)) those of a Schwarzschild
black hole. This confirms the idea that the entropy of black holes can be a
ccounted for by counting string states, and suggests that the level spacing
of the quantum states of Schwarzschild black holes is exponentially small,
and very much blurred by radiative effects.