In 1994, Bershadsky, Cecotti, Ooguri and Vafa argued that one could understand the B-model topological string on a Calabi-Yau manifold X as the partition function of a certain quantum field theory on X. I'll describe joint work with Si Li, where we provide a rigorous construction of the quantum BCOV theory on certain Calabi-Yaus. I'll also explain a result of Li: the partition function of the BCOV theory on an elliptic curve recovers the Gromov-Witten theory of the mirror curve.