Harnessing the potential of human stem cells for modelling the physiology and diseases of cortical circuitry requires monitoring cellular dynamics in vivo. Here, we show that human iPSC-derived cortical neurons transplanted in the adult mouse cortex consistently organized in large (up to ~100 mm3) vascularized neuron-glia territories with complex cytoarchitecture. Longitudinal imaging of >4000 grafted developing human neurons revealed that neuronal arbors refined via branch-specific retraction; human synaptic networks substantially restructured over 4 months, with balanced rates of synapse formation and elimination; and oscillatory population activity mirrored the patterns of fetal neural networks. Finally, we found increased synaptic stability and reduced oscillations in transplants from two individuals with Down syndrome, demonstrating the potential of in vivo imaging in human tissue grafts for patient-specific modelling of cortical development, physiology, and pathogenesis.