Earth’s rapidly changing climate creates a growing need to understand how demographic processes in natural populations are affected by climate variability, particularly among organisms threatened by extinction. Long-term, large-scale, and cross-taxon studies of vital rate variation in relation to climate variability can be particularly valuable because they can reveal environmental drivers that affect multiple species over extensive regions. Few such data exist for animals with slow life histories, particularly in the tropics, where climate variation over large-scale space is asynchronous. As our closest relatives, nonhuman primates are especially valuable as a resource to understand the roles of climate variability and climate change in human evolutionary history. Here, we provide the first comprehensive investigation of vital rate variation in relation to climate variability among wild primates. We ask whether primates are sensitive to global changes that are universal (e.g., higher temperature, large-scale climate oscillations) or whether they are more sensitive to global change effects that are local (e.g., more rain in some places), which would complicate predictions of how primates in general will respond to climate change. To address these questions, we use a database of long-term life-history data for natural populations of seven primate species that have been studied for 29–52~years to investigate associations between vital rate variation, local climate variability, and global climate oscillations. Associations between vital rates and climate variability varied among species and depended on the time windows considered, highlighting the importance of temporal scale in detection of such effects. We found strong climate signals in the fertility rates of three species. However, survival, which has a greater impact on population growth, was little affected by climate variability. Thus, we found evidence for demographic buffering of life histories, but also evidence of mechanisms by which climate change could affect the fates of wild primates.