Large-scale non-kin cooperation is a unique ingredient of human success. This type of cooperation is challenging to explain in a world of self-interested individuals. There is overwhelming empirical evidence from different disciplines that reputation and gossip promote cooperation in humans in different contexts. Despite decades of research, important details of reputation systems are still unclear. Our goal with this theme issue is to promote an interdisciplinary approach that allows us to explore and understand the evolution and maintenance of reputation systems with a special emphasis on gossip and honest signalling. The theme issue is organized around four main questions: What are the necessary conditions for reputation-based systems? What is the content and context of reputation systems? How can reputations promote cooperation? And, what is the role of gossip in maintaining reputation systems and thus cooperation?