Abstract: There are a number of conjectures regarding the all-genus Gromov-Witten theory of Calabi-Yau threefolds which have their origin in physics. While mathematical progress on these conjectures has been very slow, breakthroughs by Chang-Guo-Li and Guo-Janda-Ruan enabled proofs of some of these conjectures for the quintic. In this talk, I will describe a proof of the Yamaguchi-Yau finite generation conjecture and the BCOV holomorphic anomaly equation for smooth Calabi-Yau hypersurfaces in P(1,1,1,1,2), P(1,1,1,1,4), and P(1,1,1,2,5) and give explicit formulae for the genus one invariants.