I will discuss Topological Quantum Field Theories in two dimensions and their finite dimensional avatars - the Cohomological Quantum Field Theories of Kontsevich and Manin. I will explain how Givental gauging allows one to study geometrically the space parameterizing all CohQFTs associated with a given TQFT. In particular the gauging and the action of the renormalization group flow on this parameter space lead to a reconstruction scheme for higher genus correlators from genus zero ones. I will also discuss the effect of Mirror Symmetry and other string dualities on these spaces.