In this talk, we will discuss recent progress on the structure of the open Gromov-Witten theory of toric Calabi-Yau 3-folds relative to Aganagic-Vafa Lagrangians. For this geometry, we will present an analog of the open WDVV equations, introduced by Horev-Solomon and studied by Solomon-Tukachinsky and others, which is a system of non-linear PDEs that captures recursive relations among the open Gromov-Witten invariants. These equations are obtained via the open/closed correspondence that relates open Gromov-Witten invariants of toric Calabi-Yau 3-folds to closed Gromov-Witten invariants of toric Calabi-Yau 4-folds. Moreover, we will present the Frobenius manifold and F-manifold structures arising from the open WDVV equations and discuss their properties. This talk is based on joint work with Zhengyu Zong.