Abstract: Given a dynamical system define on the Bernoulli space (with a finite alphabet) and a potential A we can define its Gibbs measure for any given temperature. Then a natural question is the behavior of the family of Gibbs measures as function of this parameter, and specially what happens when the temperature goes to zero. We say that a measure is selected when it is the limit of a sequence of Gibbs measures. In this talk I would like to present some recent results in this field, showing some examples where selection is obtained and also discussing some cases where there is no selection.