We are witnessing an increasing interest for cooperative dynamical systems proposed in the recent literature as possible models for opinion dynamics in social and economic networks. Mathematically, they consist of a large number, N, of 'agents' evolving according to quite simple dynamical systems coupled in according to some 'locality' constraint. Each agent i maintains a time function xi(t) representing the 'opinion,' the 'belief' it has on something. As time elapses, agent i interacts with neighbor agents and modifies its opinion by averaging it with the one of its neighbors. A critical issue is the way 'locality' is modelled and interaction takes place. In Krause's model each agent can see the opinion of all the others but averages with only those which are within a threshold R from its current opinion. The main interest for these models is for N quite large. Mathematically, this means that one takes the limit for N → + ∞. We adopt an Eulerian approach, moving focus from opinions of various agents to distributions of opinions. This leads to a sort of master equation which is a PDE in the space of probabily measures; it can be analyzed by the techniques of Transportation Theory, which extends in a very powerful way the Theory of Conservation Laws. Our Eulerian approach gives rise to a natural numerical algorithm based on the `push forward' of measures, which allows one to perform numerical simulations with complexity independent on the number of agents, and in a genuinely multi-dimensional manner. We prove the existence of a limit measure as t → ∞, which for the exact dynamics is purely atomic with atoms at least at distance R apart, whereas for the numerical dynamics it is 'almost purely atomic' (in a precise sense). Several representative examples will be discussed. This is a joint work with Fabio Fagnani and Paolo Tilli.