  The c-map relates classical hypermultiplet moduli spaces in compactifications
of type II strings on a Calabi-Yau threefold to vector multiplet moduli spaces
via a further compactification on a circle. We give an off-shell description of
the c-map in N=2 superspace. The superspace Lagrangian for the hypermultiplets
is a single function directly related to the prepotential of special geometry,
and can therefore be computed using topological string theory. Similarly, a
class of higher derivative terms for hypermultiplets can be computed from the
higher genus topological string amplitudes. Our results provide a framework for
studying quantum corrections to the hypermultiplet moduli space, as well as for
understanding the black hole wave-function as a function of the hypermultiplet
moduli.
