  I review some recent work (done in collaboration with G. Veneziano) which
clarifies the existence of a correspondence between self-gravitating
fundamental string states and Schwarzschild black holes. The main result is a
detailed 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 critical
value g_c^2 = (M sqrt{alpha'})^{-1}) those of a Schwarzschild black hole. This
confirms the idea that the entropy of black holes can be accounted 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.
