  This article is a survey of a series of papers [FOOO3,FOOO4,FOOO5] in which
we developed the method of calculation of Floer cohomology of Lagrangian torus
orbits in compact toric manifolds, and its applications to symplectic topology
and to mirror symmetry. In this article we summarize the main ingredients of
calculation and illustrate them by examples. The second half of the survey is
devoted to discussion of the most recent result from [FOOO5] (arXiv:1009.1648)
where the mirror symmetry between the two Frobenius manifolds arising from the
big quantum cohomology and from the K. Saito theory of singularities was
established.
