Realizing the full utility of brain organoids as experimental systems to study human cortical development requires understanding whether organoids replicate the cellular and molecular events of this complex process precisely, reproducibly, and with fidelity to the embryo. Here we present a comprehensive single-cell transcriptomic, epigenetic, and spatial atlas of human cortical organoid development, comprising over 610,000 cells, spanning initial generation of neural progenitors through production of differentiated neuronal and glial subtypes. We define the lineage relationships and longitudinal molecular trajectories of cortical cell types during development in organoids, and show that developmental processes of cellular diversification in organoids correlate closely to endogenous ones, irrespective of metabolic state. Using this data, we identify genes with predicted human-specific roles in lineage establishment, and discover a developmental origin for the transcriptional diversity of human callosal projection neurons, a population that has undergone dramatic expansion and diversification during human evolution. Our work provides a comprehensive, single-cell molecular map of human corticogenesis in vitro, identifying developmental trajectories and molecular mechanisms associated with human cellular diversification.