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The topological recursion in the title refers to a particular formalism discovered by Eynard and Orantin in 2007. The formalism provides a concrete computational mechanism to many enumerative geometry problems, including various Hurwitz numbers, Gromov-Witten invariants of toric Calabi-Yau 3-folds, and conjecturally quantum curves (i.e., D-modules) for partition functions of topological string theory such as quantum knot invariants. The talk is aimed at presenting the predicted general consequences of the topological recursion. Per request of Albert, I will not talk about my recent papers, which give mathematically rigorous results regarding to the subject. Instead, I will try to formulate speculations and conjectures.