Pierre-Gilles de Gennes was awarded the Nobel prize in physics in 1991 for the Landau-de

Gennes theory, which generalises the well-known Oseen-Frank theory. The Ericksen-Leslie system is obtained by coupling the Navier-Stokes equations with the gradient flow for the Oseen-Frank energy. Based on the celebrated Landau-de Gennes Q-tensor theory, Beris-Edwards proposed a hydrodynamic theory to generalise the Ericksen-Leslie system from uniaxial to biaxial nematic liquid crystals. In this talk, we will give a general introduction to the Ericksen-Leslie system and the Beris-Edwards system. Then we will discuss some new mathematical results.