In the seminar we present some results on numerical approximation of macroscopic models arising in biology. In the first part we consider parabolic and quasilinear hyperbolic models of chemotaxis, which can emerge non constant steady states. We analyze such equilibria and propose a numerical scheme that is able to preserves them. We also give examples of some cases for which hyperbolic and parabolic systems have different asymptotic states. In the second part we present some open problems concerning modelling and numerical approximation of macroscopic models describing the evacuation of pedestrians from a room through a narrow exit.