A pointing gesture creates a referential triangle that incorporates distant objects into the relationship between the signaller and the gesture's recipient. Pointing was long assumed to be specific to our species. However, recent reports have shown that pointing emerges spontaneously in captive chimpanzees and can be learned by monkeys. Studies have demonstrated that both human children and great apes use manual gestures (e.g. pointing), and visual and vocal signals, to communicate intentionally about out-of-reach objects. Our study looked at how monkeys understand and use their learned pointing behaviour, asking whether it is a conditioned, reinforcement-dependent response or whether monkeys understand it to be a mechanism for manipulating the attention of a partner (e.g. a human). We tested nine baboons that had been trained to exhibit pointing, using operant conditioning. More specifically, we investigated their ability to communicate intentionally about the location of an unreachable food reward in three contexts that differed according to the human partner's attentional state. In each context, we quantified the frequency of communicative behaviour (auditory and visual signals), including gestures and gaze alternations between the distal food and the human partner. We found that the baboons were able to modulate their manual and visual communicative signals as a function of the experimenter's attentional state. These findings indicate that monkeys can intentionally produce pointing gestures and understand that a human recipient must be looking at the pointing gesture for them to perform their attention-directing actions. The referential and intentional nature of baboons' communicative signalling is discussed.