The alarm call sequences of titi monkeys (genera Plecturocebus, Callicebus and Cheracebus) have sparked important debates over whether they exhibit parallels with human language. Some researchers consider these sequences to involve both semantics and syntax, while others argue that the sequences convey semantic information without syntax. In this review, we revisit this issue by applying fine-grained linguistic analyses to the most comprehensive data set of titi monkey alarm sequences available to date. Specifically, we evaluate three competing hypotheses: one rich hypothesis suggesting that titi alarm sequences are compositional, and two deflationary alternatives. The first deflationary hypothesis holds that an alarm sequence is a single vocalisation that only superficially resembles a combination of discrete calls. The second deflationary hypothesis posits that an alarm sequence consists of a series of independent calls emitted in rapid succession, governed by no syntactic rule. The data set allows us to reject the first deflationary hypothesis but not the second, preventing us from concluding that titi monkey sequences are compositional. This leads us to another important question: if the sequences are not compositional, what information do they convey, and how? We examine the information encoded in the alarm calls and find that alarm calls likely reflect the caller’s arousal level at the time of emission of the call: A-calls encode high arousal, B-calls lower arousal, and sequences appear to track dynamic changes in arousal over time. However, strikingly, receivers still manage to extract relevant information about the event eliciting alarm sequences, likely through inferences relying on contextual cues and prior knowledge. This pragmatic enrichment suggests that emotion-based communication can give rise to complex cognitive processes, particularly on the receiver’s side.Titi monkeys thus offer a valuable model for investigating the evolutionary roots of pragmatics. More broadly, our review challenges the misconception that emotional communication is cognitively simple, and invites renewed attention to the role of affective communication in the emergence of linguistic-like abilities.