Topological field theories have long been expected to be closely related to integrable systems. A famous conjecture of Witten (proven by Kontsevich and others) states that the generating function of descendant integrals on the moduli spaces of curves is a solution to the KdV hierarchy. As a generalization of this result one may speculate a relationship between Gromov-Witten theory and integrable systems. In this talk we give a survey on this conjectural relationship and discuss some (very) low dimensional examples.