The neocortex, the seat of higher cognitive functions, exhibits a key feature across mammalian species—a highly variable degree of folding. Within the neocortex, two distinct subtypes of cortical areas can be distinguished, the isocortex and the proisocortex. Here, we have compared specific spatiotemporal aspects of folding between the proisocortex and the isocortex in 13 primates, including human, chimpanzee, and various Old World and New World monkeys. We find that folding at the boundaries of the dorsal isocortex and the proisocortex, which gives rise to the cingulate sulcus (CiS) and the lateral fissure (LF), is conserved across the primates studied and is therefore referred to as conserved folding. In contrast, the degree of folding within the dorsal isocortex exhibits huge variation across these primates, indicating that this folding, which gives rise to gyri and sulci, is subject to major changes during primate evolution. We therefore refer to the folding within the dorsal isocortex as evolved folding. Comparison of fetal neocortex development in long‐tailed macaque and human reveals that the onset of conserved folding precedes the onset of evolved folding. Moreover, the analysis of infant human neocortex exhibiting lissencephaly, a developmental malformation thought to be mainly due to abnormal neuronal migration, shows that the evolved folding is perturbed more than the conserved folding. Taken together, our study presents a two‐step model of folding that pertains to primate neocortex development and evolution. Specifically, our data imply that the conserved folding and the evolved folding constitute two distinct, sequential events.