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This paper presents Networks of Influence Diagrams (NID), a compact, natural and highly expressive language for reasoning about agents' beliefs and decision-making processes. NIDs are graphical structures in which agents' mental models are represented as nodes in a network; a mental model for an agent may itself use descriptions of the mental models of other agents. NIDs are demonstrated by examples, showing how they can be used to describe conflicting and cyclic belief structures, and certain forms of bounded rationality. In an opponent modeling domain, NIDs were able to outperform other computational agents whose strategies were not known in advance. NIDs are equivalent in representation to Bayesian games but they are more compact and structured than this formalism. In particular, the equilibrium definition for NIDs makes an explicit distinction between agents' optimal strategies, and how they actually behave in reality.