Primates and rodents, which descended from a common ancestor around 90 million years ago, exhibit profound differences in behaviour and cognitive capacity; the cellular basis for these differences is unknown. Here we use single-nucleus RNA sequencing to profile RNA expression in 188,776 individual interneurons across homologous brain regions from three primates (human, macaque and marmoset), a rodent (mouse) and a weasel (ferret). Homologous interneuron types-which were readily identified by their RNA-expression patterns-varied in abundance and RNA expression among ferrets, mice and primates, but varied less among primates. Only a modest fraction of the genes identified as 'markers' of specific interneuron subtypes in any one species had this property in another species. In the primate neocortex, dozens of genes showed spatial expression gradients among interneurons of the same type, which suggests that regional variation in cortical contexts shapes the RNA expression patterns of adult neocortical interneurons. We found that an interneuron type that was previously associated with the mouse hippocampus-the 'ivy cell', which has neurogliaform characteristics-has become abundant across the neocortex of humans, macaques and marmosets but not mice or ferrets. We also found a notable subcortical innovation: an abundant striatal interneuron type in primates that had no molecularly homologous counterpart in mice or ferrets. These interneurons expressed a unique combination of genes that encode transcription factors, receptors and neuropeptides and constituted around 30% of striatal interneurons in marmosets and humans.