The nematic (uniaxial) liquid crystal flows are often described by the classical Ericksen-Leslie theory. Even in the (over) simplified model case, it is given by a highly nonlinear coupling of the Navier-Stokes system and the system for the (heat) flow of harmonic maps. Both of these two systems were studied by numerous authors, and much of the earlier theory developed for the dynamics of liquid crystals were based on. In this talk, I am going to describe some recent studies on the flows of liquid crystals and their consequences in the heat flow of harmonic maps.