In this talk I will present some results concerning the well-posedness and asymptotic behaviour of some evolution equations  arising in the modelling of opinion formation.
More precisely, imagine a group of individuals  debating over some question. As a result of interactions among individuals, the distribution of opinion, a priori a general probability measure, is not static but evolves in time. 
The problem is then to study the long-time behaviour of this distibution from the knowledge of the interaction rules.
I will first introduce the main ideas and techniques based on Boltzmann-like equation with a very simple model.
Then I will present various possible extensions and some theoretical results I obtained with my collaborators in Argentina concerning the long time behaviour the distribution and the rate of convergence to the stationary state.