Calabi-Yau manifolds have been used for over 30 years as a primary way of compactifying string theory to give semi-realistic models of physics in four dimensions. This talk describes recent progress in using the geometry of elliptic fibrations through the approach known as F-theory to better understand the physics of a broad class of nonperturbative string compactifications, to identify ways in which the Standard Model of particle physics arises naturally in this context, and to shed light on the structure of the largest known set of Calabi-Yau manifolds. In particular, the talk will describe a recent complete analysis the full set of 470 million toric hypersurface Calabi-Yau threefolds, of which over 99.99% have an elliptic or genus one fiber structure. This approach also helps understand the way in which all of these Calabi-Yaus are connected, and provides strong evidence that the set of such manifolds is finite. This talk describes recent work with Shing Yan Li and with Fatima Abbasi and Richard Nally, and upcoming work with Lara Anderson, James Gray, and Richard Nally.