Abstract The collective motion of various organisms like the flocking of birds (Fig. 6.1) [1], the swimming of schools of fish [2], and the motion of herds of quadrupeds, migrating bacteria (§4.1 ), ants [3] or pedestrians (§6.2) is a fascinating phenomenon catching our eyes when we observe our natural environment. In addition to the aesthetic aspects, studies on this collective behaviour can have interesting applications as well, e.g., modelling the motion of a crowd of people can help urban designers. Here we address the question whether there are some global, perhaps universal, features of this type of behaviour when many organisms are involved and parameters like the level of perturbations or the mean distance between the individuals are changed.