  In this lecture we summarize some recent work on the understanding of
instanton effects in string theories with 16 supersymmetries. In particular, we
consider F^4 couplings using the duality between the heterotic string on T^4
and type IIA on K_3 at an orbifold point, as well as higher and lower
dimensional versions of this string-string duality. At the perturbative level a
non-trivial test of the duality, requiring several miraculous identities, is
presented by matching a purely one-loop heterotic amplitude to a purely
tree-level type II result. A wide variety of non-perturbative effects is shown
to occur in this setting, including D-brane instantons for type IIA on K_3 x
S^1 and NS5-brane instantons for type IIA on K_3 x T^2. Moreover, the analysis
of the three-dimensional case, which possesses a non-perturbative SO(8,24,Z)
U-duality, reveals the presence of Kaluza-Klein 5-brane instanton effects, both
on the heterotic and the type II side.
