Animal communication is first and foremost about signal transmission and aims to understand how communication occurs. It is a field that has contributed to and been inspired by other fields, from information technology to neuroscience, in finding ever better methods to eavesdrop on the actual ‘message’ that forms the basis of communication. Much of this review deals with vocal communication as an example of the questions that research on communication has tried to answer and it provides an historical overview of the theoretical arguments proposed. Topics covered include signal transmission in different environments and different species, referential signaling, and intentionality. The contention is that animal communication may reveal significant thought processes that enable some individuals in a small number of species so far investigated to anticipate what conspecifics might do, although some researchers think of such behavior as adaptive or worth dismissing as anthropomorphizing. The review further points out that some species are more likely than others to develop more complex communication patterns. It is a matter of asking how animals categorize their world and which concepts require cognitive processes and which are adaptive. The review concludes with questions of life history, social learning, and decision making, all criteria that have remained relatively unexplored in communication research. Long‐lived, cooperative social animals have so far offered especially exciting prospects for investigation. There are ample opportunities and now very advanced technologies as well to tap further into expressions of memory of signals, be they vocal or expressed in other modalities.WIREs Cogn Sci2014, 5:661–677. doi: 10.1002/wcs.1321This article is categorized under:Cognitive Biology > Evolutionary Roots of CognitionNeuroscience > BehaviorNeuroscience > Cognition