The study of human cortical development has major implications for brain evolution and diseases but has remained elusive due to paucity of experimental models. Here we found that human embryonic stem cells (ESCs) and induced pluripotent stem cells (iPSCs), cultured without added morphogens, recapitulate corticogenesis leading to the sequential generation of functional pyramidal neurons of all six layer identities. After transplantation into mouse neonatal brain, human ESC-derived cortical neurons integrated robustly and established specific axonal projections and dendritic patterns corresponding to native cortical neurons. The differentiation and connectivity of the transplanted human cortical neurons complexified progressively over several months in vivo, culminating in the establishment of functional synapses with the host circuitry. Our data demonstrate that human cortical neurons generated in vitro from ESC/iPSC can develop complex hodological properties characteristic of the cerebral cortex in vivo, thereby offering unprecedented opportunities for the modeling of human cortex diseases and brain repair.