The complete structure of the moduli space of \cys\ and the associated
Landau-Ginzburg theories, and hence also of the corresponding low-energy
effective theory that results from (2,2) superstring compactification, may be
determined in terms of certain holomorphic functions called periods. These
periods are shown to be readily calculable for a great many such models. We
illustrate this by computing the periods explicitly for a number of classes of
\cys. We also point out that it is possible to read off from the periods
certain important information relating to the mirror manifolds.