  We review several aspects of heterotic, type II, F-theory, and M-theory
compactifications on Calabi-Yau threefolds and fourfolds. In the context of
dualities we focus on the heterotic gauge structure determined by the various
types of fibration relevant in the framework of heterotic/type II duality in
D=4 as well as 4D F-theory. We also consider transitions between Calabi-Yau
manifolds in both three and four dimensions and review some of the consequences
for the behavior of the superpotential.
