‘Language’ and ‘cognition’, the two words from the title of the present volume, could both be used to characterize human beings. To the best of our knowledge, we are the only creatures on this planet to make use of a communication system meeting the complexity of natural languages. All research that has been done in the sixties and seventies of the previous century to assess the language capacity of chimpanzees converges on the conclusion that these animals can learn some 100 to 150 words but that they never achieve the level where they realize the symbolic status of these words. Words are not mere members in an associate pairing with the thing they refer to, but represent the concept behind these referents in some code system (e.g., speech, signs, …). Nor did the animals succeed in constructing word strings in accordance with syntactic rules. Both symbolic behavior (Deacon 1997) and syntactic capacity (Chomsky 1965), which some researchers consider as a particular manifestation of symbolic representation at a higher organizational level (Deacon 1997; Langacker 1990; this volume), characterize human language. Hence, despite the many capabilities of great apes, they lack the capacity for natural language. In a Science paper thirty years ago, Herb Terrace and his colleagues critically analysed researchers’ attempts to teach great apes to make use of language and concluded that they dismally fail when judged against the critical dimensions that define natural languages: “Apes can learn many isolated symbols (as can dogs, horses, and other nonhuman species), but they show no unequivocal evidence of mastering the conversational, semantic, or syntactic organization of language.” (Terrace, Petitto, Sanders, & Bever 1979: 902). Today, no evidence has appeared to suggest that this conclusion needs to be changed.