Physics predicts that the Gromov-Witten theory of Calabi-Yau threefolds satisfies two fundamental properties: Finite generation and a holomorphic anomaly equation. I will explain a recent conjecture with Pixton that extends these conjectures to all elliptic fibrations, and indicate how to prove it in several basic cases. If time permits, we will also discuss holomorphic anomaly equations for hyper-Kaehler varieties.