The field of primate cognition studies how primates, including humans, perceive, process, store, retrieve, and use information to guide decision making and other behavior. Much of this research is motivated by a desire to understand how these abilities evolved. Large and diverse samples from a wide range of species are vital to achieving this goal. In reality, however, primate cognition research suffers from small sample sizes and is often limited to a handful of species, which constrains the evolutionary inferences we can draw. We conducted a systematic review of primate cognition research published between 2014 and 2019 to quantify the extent of this problem. Across 574 studies, the median sample size was 7 individuals. Less than 15% of primate species were studied at all, and only 19% of studies included more than one species. Further, the species that were studied varied widely in how much research attention they received, partly because a small number of test sites contributed most of the studies. These results suggest that the generalizability of primate cognition studies may be severely limited. Publication bias, questionable research practices, and a lack of replication attempts may exacerbate these problems. We describe the ManyPrimates project as one approach to overcoming some of these issues by establishing an infrastructure for large-scale collaboration in primate cognition research. Building on similar initiatives in other areas of psychology, this approach has already yielded one of the largest and most diverse primate samples to date and enables us to ask many research questions that can only be addressed through collaboration.