Primate brains vary dramatically in size and organization, but the genetic and developmental basis for these differences has been difficult to study due to lack of experimental models. Pluripotent stem cells and brain organoids provide a potential opportunity for comparative and functional studies of evolutionary differences, particularly during the early stages of neurogenesis. However, many challenges remain, including isolating stem cell lines from additional great ape individuals and species to capture the breadth of ape genetic diversity, improving the reproducibility of organoid models to study evolved differences in cell composition and combining multiple brain regions to capture connectivity relationships. Here, we describe strategies for identifying evolved developmental differences between humans and non-human primates and for isolating the underlying cellular and genetic mechanisms using comparative analyses, chimeric organoid culture, and genome engineering. In particular, we focus on how organoid models could ultimately be applied beyond studies of progenitor cell evolution to decode the origin of recent changes in cellular organization, connectivity patterns, myelination, synaptic development, and physiology that have been implicated in human cognition.