  In this article we review four-dimensional string vacua with N=2 space-time
supersymmetry. In particular, we will discuss several aspects of the
string-string duality between the heterotic string, compactified on $K3\times
T^2$, and the type II superstring compactified on a Calabi-Yau three-fold. We
investigate the massless supersymmetric spectra, showing agreement for a large
class of dual heterotic/type II string pairs. Some emphasis is given to
non-perturbative heterotic phenomena, such as non-perturbative transitions
among different vacua and strong coupling singularities, and to their geometric
Calabi-Yau description on the type II side. We compare the effective N=2
supergravity actions of dual heterotic/type II string compactifications, and
show that the N=2 prepotentials and also higher order gravitational couplings
nicely agree in the weak heterotic coupling limit. Finally we consider extremal
black hole solutions of N=2 supergravity which arise in the context of
heterotic or type II N=2 compactifications. For the type II backgrounds we show
how the entropies of these black holes depend on the topological data of the
underlying Calabi-Yau spaces; we also construct massless black holes which are
relevant for the conifold transition among different Calabi-Yau vacua.
