  The paper studies three classes of Frobenius manifolds: Quantum Cohomology
(topological sigma-models), unfolding spaces of singularities (K. Saito's
theory, Landau-Ginzburg models), and the recent Barannikov-Kontsevich
construction starting with the Dolbeault complex of a Calabi-Yau manifold and
conjecturally producing the B--side of the Mirror Conjecture in arbitrary
dimension. Each known construction provides the relevant Frobenius manifold
with an extra structure which can be thought of as a version of ``non-linear
cohomology''. The comparison of thesestructures sheds some light on the general
Mirror Problem: establishing isomorphisms between Frobenius manifolds of
different classes. Another theme is the study of tensor products of Frobenius
manifolds, corresponding respectively to the K\"unneth formula in Quantum
Cohomology, direct sum of singularities in Saito's theory, and presumably, the
tensor product of the differential Gerstenhaber-Batalin-Vilkovisky algebras. We
extend the initial Gepner's construction of mirrors to the context of Frobenius
manifolds and formulate the relevant mathematical conjecture.
