From cells to societies, several general principles arise again and again that facilitate cooperation and suppress conflict. In this study, I describe three general principles of cooperation and how they operate across systems including human sharing, cooperation in animal and insect societies and the massively large-scale cooperation that occurs in our multicellular bodies. The first principle is that of Walk Away: that cooperation is enhanced when individuals can leave uncooperative partners. The second principle is that resource sharing is often based on the need of the recipient (i.e., need-based transfers) rather than on strict account-keeping. And the last principle is that effective scaling up of cooperation requires increasingly sophisticated and costly cheater suppression mechanisms. By comparing how these principles operate across systems, we can better understand the constraints on cooperation. This can facilitate the discovery of novel ways to enhance cooperation and suppress cheating in its many forms, from social exploitation to cancer.