The last 20 years have seen an enormous amount of research on social dilemmas on networks, originating from the 1992 paper by Nowak and May on the emergence of cooperation on a Prisoner’s Dilemma on a lattice. It has been only recently that most of the (often contradictory) theoretical predictions have been put to the test of experiments. In this talk I will present experimental results about Prisoner’s Dilemma on fixed networks, both regular and complex, that show that the existence of a fixed population structure does not influence the amount of observed cooperation. I will also show experiments in which we look deep for the reasons for this result and for its generality, by working with small groups and with populations of different ages. Finally, I will devote the last part of my talk to discuss the case in which players can change their links in the network, where an almost full cooperative population has been observed experimentally. To that end, I will present preliminary experimental results, some of three weeks ago, that strongly suggest that the driver of cooperation is reputation and not the possibility to rewire connections.