Several approaches have recently been proposed for learning decentralized deep multiagent policies that coordinate via a differentiable communication channel. While these policies are effective for many tasks, interpretation of their induced communication strategies has remained a challenge. Here we propose to interpret agents' messages by translating them. Unlike in typical machine translation problems, we have no parallel data to learn from. Instead we develop a translation model based on the insight that agent messages and natural language strings mean the same thing if they induce the same belief about the world in a listener. We present theoretical guarantees and empirical evidence that our approach preserves both the semantics and pragmatics of messages by ensuring that players communicating through a translation layer do not suffer a substantial loss in reward relative to players with a common language.