Rich data gathered in experimental primatology in the last 40 years are beginning to benefit from analytical methods used in contemporary linguistics, especially in the area of semantics and pragmatics. These methods have started to clarify five questions: (i) What morphology and syntax, if any, do monkey calls have? (ii) What is the ‘lexical meaning’ of individual calls? (iii) How are the meanings of individual calls combined? (iv) How do calls or call sequences compete with each other when several are appropriate in a given situation? (v) How did the form and meaning of calls evolve? Four case studies from this emerging field of ‘primate linguistics’ provide initial answers, pertaining to Old World monkeys (putty-nosed monkeys, Campbell’s monkeys, and colobus monkeys) and New World monkeys (black-fronted Titi monkeys). The morphology mostly involves simple calls, but in at least one case (Campbell’s -oo) one finds a root–suffix structure, possibly with a compositional semantics. The syntax is in all clear cases simple and finite-state. With respect to meaning, nearly all cases of call concatenation can be analyzed as being semantically conjunctive. But a key question concerns the division of labor between semantics, pragmatics, and the environmental context (‘world’ knowledge and context change). An apparent case of dialectal variation in the semantics (Campbell’s krak) can arguably be analyzed away if one posits sufficiently powerful mechanisms of competition among calls, akin to scalar implicatures. An apparent case of noncompositionality (putty-nosed pyow–hack sequences) can be analyzed away if one further posits a pragmatic principle of ‘urgency’. Finally, rich Titi sequences in which two calls are re-arranged in complex ways so as to reflect information about both predator identity and location are argued not to involve a complex syntax/semantics interface, but rather a fine-grained interaction between simple call meanings and the environmental context. With respect to call evolution, the remarkable preservation of call form and function over millions of years should make it possible to lay the groundwork for an evolutionary monkey linguistics, illustrated with cercopithecine booms.