Efficiently handling reputation is important in dealing with free-riding, malicious attacks and random failures in self-organized communication systems. At the same time, work in this context is often found to be relevant in many other disciplines, in particular the social sciences. A number of distributed reputation systems have been proposed and analyzed, although research has not been very coherent. In this paper, for the first time, we provide an overview of the state-of-the-art in the various computer science communities as well as the social sciences. In particular, we present results obtained from our mathematical model devised to investigate the impact of liars on their peers' reputation about a subject. We find that liars have no impact unless their number exceeds a certain threshold (phase transition). We give precise formulae and quantify the impact, thereby providing insight into fundamental questions in social networks as well as facilitating performance evaluation and optimization of distributed reputation systems in communication networks. We conclude by suggesting fundamental directions for future research into reputation.