  The mathematical idea of resurgence allows one to obtain nonperturbative
information from the large-order behavior of perturbative expansions. This idea
can be very fruitful in physics applications, in particular if one does not
have access to such nonperturbative information from first principles. An
important example is topological string theory, which is a priori only defined
as an asymptotic perturbative expansion in the coupling constant g_s. We show
how the idea of resurgence can be combined with the holomorphic anomaly
equation to extend the perturbative definition of the topological string and
obtain, in a model-independent way, a large amount of information about its
nonperturbative structure.
