We study the ubiquity of multiple fibration structures in known constructions of Calabi-Yau manifolds and explore the role they play in string dualities. In particular, upon analyzing a set of F-theory effective theories associated to the different elliptic fibrations, we relate them via the F-/M-theory correspondence. Along the same line, a systematic approach to classifying/enumerating elliptic fibrations will also be addressed. Finally, if time permits, some comments will be given on the geometry/physics of non-flat fibrations, which appear rather genericall! y in this context.