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A multiplicity of visual languages have been proposed for representing business models. These languages are claimed to facilitate tasks such as understanding, communicating, and innovating a business model; and have been developed rather independently by scholars from accounting, computer science, information systems, and strategy. Consequently, the existing approaches greatly differ and to some extent contradict each other, for example, regarding their understanding of the business model concept, their terminology, and their visual notations–which means there is little common ground for developing a cumulative stream of research. Therefore, we provide a systematic, cross-disciplinary review of this emerging field and synthesize the pragmatic, semantic, and syntactic foundations of the proposed approaches. Further, we derive an agenda for future research and discuss the challenges that lie ahead to advance the field.