Many examples of Calabi-Yau manifolds have been constructed. These are partially classified by the Hodge numbers (h^11, h^21). A plot of these numbers reveals interesting structure, for the case that the Hodge numbers are large. I will 'explain' some of this structure in terms of the fibration structure of the manifolds. At the other end of the distribution, finding manifolds with small Hodge numbers seems to be synonymous with finding manifolds with large groups of freely acting symmetries. These seem to be rare. I will discuss some constructions of what may be the simplest Calabi-Yau manifolds.