One result of the fruitful interaction between Quantum Field Theory and Algebraic Geometry was the creation of Frobenius manifolds. Those objects lie at the heart of the mathematical vision of mirror symmetry and Topological Field Theory. Recent results allow to go beyond this perspective. Namely, a new source of Frobenius manifolds has been discovered. The richness of this allows unexpected bridges between the domain of Algebraic Geometry and Information Geometry (involving Gromov—Witten like invariants, moduli spaces of curves, webs, Hessian geometry). Furthermore, quantum Frobenius manifolds can be introduced. These aspects include the emergence of F–manifolds, and motivic enrichments. In particular, this leads to explore new research paths. From this emerge new perspectives on Frobenius manifolds and places them in the center of important conjectures.
