  The BKMP Remodeling Conjecture \cite{Ma,BKMP09,BKMP10} predicts all genus
open-closed Gromov-Witten invariants for a toric Calabi-Yau $3$-orbifold by
Eynard-Orantin's topological recursion \cite{EO07} on its mirror curve. The
proof of the Remodeling Conjecture by the authors \cite{FLZ1,FLZ3} relies on
comparing two Feynman-type graph sums in both A and B-models. In this paper, we
will survey these graph sum formulae and discuss their roles in the proof of
the conjecture.
