It is shown that homotopical algebra structures can be considered as a classical limits of BV master equations. This leads to the notion of quantum homotopical structures. It is shown that BV integral leads to induced quantum homotopical structures and classical limit of this construction are Kadeishvili-type theorems. WDVV equations are considered as a homotopical algebraic structures, and Kodaira-Spenser theory is treated as a version of BV integral. In this way we recover Barannikov-Kontsevich construction of solution to WDVV and generalize it to 1-loop construction obtaining solutions to Getzler equations.