Research in formal theoretical semantics has recently expanded its scope to include gestural communication, focusing in particular on gestures that contribute to the content of an accompanying utterance, e.g., size gestures (LARGE, WIDE), pointing gestures, and gestures that depict objects (TELESCOPE) or actions (SLAP). At the same time, fruitful inquiries at the intersection of primatology and linguistics have given rise to the hypothesis that human and non-human great apes share a common set of directive (=imperative) gestures. Directive gestures such as (...) STOP or COME-CLOSER, pose non-trivial issues for a semantic analysis: we inherit the challenges that pertain to the analysis of imperative utterances (Come closer!), while adding a further challenge that stems from the underspecified mapping between a directive body movement and its potential counterparts in human language. We begin by outlining the problem and surveying the nascent state-of-the-art with regards to a formal semantics of directive gestures. Particular attention is given to the multifunctionality of directive gestures, which typically have different effects in different contexts; for example, a non-human ape gesture may communicate "Stop that" in some contexts and "Move away" in others, with similar patterns found in humans. We show that this multifunctionality can be derived from a single, rich abstract lexical entry, "Not…!", a candidate for a universal building block of meaning, shared by human and non-human great apes. "Not…!", which incorporates negation/rejection, temporal reference and presuppositionality is more explanatory in comparison to a minimal alternative. This chapter lays out the hypothesis space, addressing the foundational question of how to explain attested gestural overlap between human and non-human great apes. We conclude the chapter by reviewing potential expansions of the analysis to the pragmatic gestures of humans, which are thus placed on the primate gestural meaning continuum and connected to the directive gestures we share with our non-human relatives in the great ape family. (shrink)