The existance of quantum ring structure was first suggested by C. Vafa in 1990. Later on, it was reformulated by E. Witten and rigorously proved by Y. Ruan and G. Tian and later by other people. The crutial step is the construction of Gromov-Witten invariants for Kahler (or more generally symplectic) manifolds. These are certain counts of pseudo-holomomorphic curves inside the given manifold X (for a generic almost complex structure J on the tangent bundle TX of X) satisfying some fixed combinatorial conditions. I will sketch the main ideas in the construction of GW-invariants, and their relevance to the construction of quantum cup product. Then I will try to present the new ideas/directions in constructing refined versions of GW-invariants. All these constructions are motivated by a conjecture of R. Gopakumar and C. Vafa which relates the BPS-states with the GW-invariants.