Relations in tautological ring of moduli spaces of stable curves can produce universal equations for Gromov-Witten invariants for all compact symplectic manifolds. A typical example of such equations is the WDVV equation, which is a genus-0 equation and gives the associativity of the quantum cohomology. Finding such relations in higher genera is a very difficult problem. I will talk about some topological recursion relations for all genera which was proved in a joint paper with R. Pandharipande. Some of these relations can be used to prove a conjecture of Kefeng Liu and Hao Xu.