  Nonperturbative effects in string theory are usually associated to D-branes.
In many cases it can be explicitly shown that D-brane instantons control the
large-order behavior of string perturbation theory, leading to the well-known
(2g)! growth of the genus expansion. This paper presents a detailed treatment
of nonperturbative solutions in string theory, and their relation to the
large-order behavior of perturbation theory, making use of transseries and
resurgent analysis. These are powerful techniques addressing general
nonperturbative contributions within non-linear systems, which are developed at
length herein as they apply to string theory. The cases of topological strings,
the Painleve I equation describing 2d quantum gravity, and the quartic matrix
model, are explicitly addressed. These results generalize to minimal strings
and general matrix models. It is shown that, in order to completely understand
string theory at a fully nonperturbative level, new sectors are required beyond
the standard D-brane sector.
