As highlighted by several contributions to this special issue, there is still ongoing debate about the number, exact location, and boundaries of the visual areas located in cortex immediately rostral to the second visual area (V2), i.e., the “third tier” visual cortex, in primates. In this review, we provide a historical overview of the main ideas that have led to four models of third tier cortex organization, which are at the center of today's debate. We formulate specific predictions of these models, and compare these predictions with experimental evidence obtained primarily in New World primates. From this analysis, we conclude that only one of these models (the “multiple-areas” model) can accommodate the breadth of available experimental evidence. According to this model, most of the third tier cortex in New World primates is occupied by two distinct areas, both representing the full contralateral visual quadrant: the dorsomedial area (DM), restricted to the dorsal half of the third visual complex, and the ventrolateral posterior area (VLP), occupying its ventral half and a substantial fraction of its dorsal half. DM belongs to the dorsal stream of visual processing, and overlaps with macaque parietooccipital (PO) area (or V6), whereas VLP belongs to the ventral stream and overlaps considerably with area V3 proposed by others. In contrast, there is substantial evidence that is inconsistent with the concept of a single elongated area V3 lining much of V2. We also review the experimental evidence from macaque monkey and humans, and propose that, once the data are interpreted within an evolutionary-developmental context, these species share a homologous (but not necessarily identical) organization of the third tier cortex as that observed in New World monkeys. Finally, we identify outstanding issues, and propose experiments to resolve them, highlighting in particular the need for more extensive, hypothesis-driven investigations in macaque and humans.