We will explain the notion of exact controllability to trajectories and the main mathematical difficulties which are closely related (without going into technical details); We will give some recent results obtained in this direction for equations of fluid mechanics. An interesting point is the relation of this concept to a non standard approach of a data assimilation problem: if you know the (value of the) solution y of an evolution problem on a (small) subdomain Ω0​ during a period of time (0,T) can you determine the value of y(t0​) on the whole domain Ω? The usual question is set for t0​=0 and this gives an ill-posed problem while we show (for some important examples) that for any t0​>0, it corresponds to a well-posed problem. This is of major importance for many applications, for example for simulation of meteorological models.