Efficient derivation of human cerebral neocortical neural stem cells (NSCs) and functional neurons from pluripotent stem cells (PSCs) facilitates functional studies of human cerebral cortex development, disease modeling and drug discovery. Here we provide a detailed protocol for directing the differentiation of human embryonic stem cells (hESCs) and induced pluripotent stem cells (iPSCs) to all classes of cortical projection neurons. We demonstrate an 80-d, three-stage process that recapitulates cortical development, in which human PSCs (hPSCs) first differentiate to cortical stem and progenitor cells that then generate cortical projection neurons in a stereotypical temporal order before maturing to actively fire action potentials, undergo synaptogenesis and form neural circuits in vitro. Methods to characterize cortical neuron identity and synapse formation are described.