  We argue that the Gopakumar-Vafa interpretation of the topological string
partition function can be used to compute and resum certain non-perturbative
brane instanton effects of type II CY compactifications. In particular the
topological string A-model encodes the non-perturbative corrections to the
hypermultiplet moduli space metric from general D1/D(-1)-brane instantons in 4d
N=2 IIB models. We also discuss the reduction to 4d N=1 by fluxes and/or
orientifolds and/or D-branes, and the prospects to resum brane instanton
contributions to non-perturbative superpotentials. We argue that the connection
between non-perturbative effects and the topological string underlies the
continuity of non-perturbative effects across lines of BPS stability. We also
confirm this statement in mirror B-model matrix model examples, relating matrix
model instantons to non-perturbative D-brane instantons. The computation of
non-perturbative effects from the topological string requires a 3d circle
compactification and T-duality, relating effects from particles and instantons,
reminiscent of that involved in the physical derivation of the
Kontsevich-Soibelmann wall-crossing formula.
