Cooperative relationships arise from a history of mutually beneficial interactions between individuals, and they enable cooperation among a range of entities, including biological organisms, business firms, and nation-states. As one of the simplest of emergent social forms, cooperative relationships can possess higher level properties (e.g., common expectations and rules of interaction, shared communication protocols) that are more than the sum of individual interactions. As such, cooperative relationships can become “things” in their own right, shaping how partners treat each other and how others treat partners within a relationship. Many open questions remain about how the emergent properties of cooperative relationships arise and how they foster future beneficial interactions while mitigating the risk of exploitation. Here, we frame these diverse findings and emerging questions in terms of the inputs and algorithms that partners use in forming models of each other and in guiding behaviors toward each other. We finish by outlining areas ripe for future exploration.