An expansion of the cerebral neocortex is thought to be the foundation for the unique intellectual abilities of humans. It has been suggested that an increase in the proliferative potential of neural progenitors (NPs) underlies the expansion of the cortex and its convoluted appearance. Here we show that increasing NP proliferation induces expansion and folding in an in vitro model of human corticogenesis. Deletion of PTEN stimulates proliferation and generates significantly larger and substantially folded cerebral organoids. This genetic modification allows sustained cell cycle re-entry, expansion of the progenitor population, and delayed neuronal differentiation, all key features of the developing human cortex. In contrast, Pten deletion in mouse organoids does not lead to folding. Finally, we utilized the expanded cerebral organoids to show that infection with Zika virus impairs cortical growth and folding. Our study provides new insights into the mechanisms regulating the structure and organization of the human cortex.