The visual image transmitted by the retina to the brain has long been understood in terms of spatial filtering by the center-surround receptive fields of retinal ganglion cells (RGCs). Recently, this textbook view has been challenged by the stunning functional diversity and specificity observed in ∼40 distinct RGC types in the mouse retina. However, it is unclear whether the ∼20 morphologically and molecularly identified RGC types in primates exhibit similar functional diversity, or instead exhibit center-surround organization at different spatial scales. Here, we reveal striking and surprising functional diversity in macaque and human RGC types using large-scale multi-electrode recordings from isolated macaque and human retinas. In addition to the five well-known primate RGC types, 18-27 types were distinguished by their functional properties, likely revealing several previously unknown types. Surprisingly, many of these cell types exhibited striking non-classical receptive field structure, including irregular spatial and chromatic properties not previously reported in any species. Qualitatively similar results were observed in recordings from the human retina. The receptive fields of less-understood RGC types formed uniform mosaics covering visual space, confirming their classification, and the morphological counterparts of two types were established using single-cell recording. The striking receptive field diversity was paralleled by distinctive responses to natural movies and complexity of visual computation. These findings suggest that diverse RGC types, rather than merely filtering the scene at different spatial scales, instead play specialized roles in human vision.