We report on the recent progress in computing the effective supergravity
action from superstring scattering amplitudes beyond the tree approximation. We
discuss the moduli-dependent string loop corrections to gauge, gravitational
and Yukawa couplings.Comment: 11 pages, CPTH-C218.0193 (Based on talks presented at the Rome
Workshop STRINGS 92, at the 7th Meeting of the American Physical Society, and
at the 26th Erice Workshop: ``From Superstrings to Supergravity"
