  Non-perturbative corrections and modular properties of four-dimensional type
IIB Calabi-Yau orientifolds are discussed. It is shown that certain
non-perturbative alpha' corrections survive in the large volume limit of the
orientifold and periodically correct the Kahler potential. These corrections
depend on the NS-NS two form and have to be completed by D-instanton
contributions to transform covariantely under symmetries of the type IIB
orientifold background. It is shown that generically also the D-instanton
superpotential depends on the two-form moduli as well as on the complex
dilaton. These contributions can arise through theta-functions with the dilaton
as modular parameter. An orientifold of the Enriques Calabi-Yau allows to
illustrate these general considerations. It is shown that this compactification
leads to a controlled four-dimensional N=1 effective theory due to the absence
of various quantum corrections. Making contact to the underlying topological
string theory the D-instanton superpotential is proposed to be related to a
specific modular form counting D3, D1, D(-1) degeneracies on the Enriques
Calabi-Yau.
