We discuss some aspects of F-theory in four dimensions on elliptically
fibered Calabi-Yau fourfolds which are Calabi-Yau threefold fibration
s, A particularly simple class of such manifolds emerges for fourfolds
in which the generic Calabi-Yau threefold fiber is itself an elliptic
fibration and is K3 fibered. Duality between F-theory compactified on
Calabi-Yau fourfolds and heterotic strings on Calabi-Yau threefolds p
uts constraints on the cohomology of the fourfold. By computing the He
dge diamond of Calabi-Yau fourfolds we provide first numerical evidenc
e for F-theory dualities in four dimensions.