In the last 40 years, field experiments in primatology have yielded rich data on the form and function of non-human primate alarm calls. We will review extant results and argue by way of case studies that these data are ripe for explicit formal models using the techniques of contemporary linguistics. While this methodological goal is largely independent from the issue of the evolutionary connection between human and primate languages, we will show that within some subfamilies (=cercopitheci), an 'evolutionary linguistics' could be developed, thanks to the extraordinary conservation of call form and function across millions of years. Following the methods outlined in Schlenker et al. 2014, we will develop fragments for call systems found in Old World monkeys (Campbell's monkeys, Putty-nosed monkeys, Black-and-White/King Colobus monkeys) and New World monkeys (Titis), and we will discuss recent results pertaining to the alarm calls and communicative gestures of apes (chimpanzees, bonobos, gorillas).