The computation of the Gromov-Witten (GW) invariants of the compact Calabi Yau 3-folds is a central and yet difficult problem in geometry and physics. In a seminal work in 1993, Bershadsky, Cecotti, Ooguri and Vafa (BCOV) introduced the higher genus B-model in physics. During the subsequent years, a series of conjectural formulae was proposed by physicists based on the BCOV B-model, which effectively calculates the higher genus GW potential from lower genus GW potentials and a finite ambiguity. In this talk, we will introduce some recent mathematical progresses in this direction. This talk is based on the joint works with Chang-Li-Li and the joint works with Janda-Ruan.