The formation of functional neuronal networks is one of the key aspects of neuronal network development. During development, neurons typically undergo a phase of over-connectivity followed by synaptic pruning and a reduction in neuronal connectivity. Similarly, network activity undergoes different phases of synchronous oscillatory firing before complex firing patterns emerge. The functional role of this stereotypic oscillatory network activity is not fully understood however it is believed that synchronous activity is important to shape neuronal connectivity and the development of mature neuronal networks. Human pluripotent (PSC) stem cells can be terminally differentiated into cerebral cortex neurons in vitro. These neurons express marker from all cortical layer, form functional synapses and acquire mature electrophysiological properties over time. We used calcium imaging to monitor neuronal network activity in these neurons over weeks. We found that human PSC-derived cortical neurons form large-scale networks in vitro that reflect those found in the developing cerebral cortex. Synchronised oscillatory networks developed in a highly stereotyped pattern over several weeks in culture. An initial phase of increasing frequency was followed by a phase of decreasing frequency, before giving rise to non-synchronous, highly recurrent, mature firing pattern. Blocking AMPA or NMDA receptors indicated that synchronous firing is a result of excitatory network activity. We investigated single neuron connectivity using a trans-synaptic rabies tracing technique. Most neurons received inputs from only a few other neurons. A small subset of hub like neurons however received a large number of synaptic inputs indicating that the connectivity in these networks follows a power law distribution. These data shows that the formation of PSC-derived cortical networks in vitro mimics cortical network development and function and can be used to study network dynamics in health and disease. Down syndrome (DS) is the most common form of intellectual disability and in the majority of cases is caused by Trisomy 21 (TS21). To date, little is known about the developmental and functional basis of this neurological disorder. We used TS21 stem cell derived cortical neurons to model cortical network development in DS and compared it to euploid control cells. We found that TS21 neurons displayed deficiencies in cortical network synchronisations as well as in complex network dynamics suggesting that aberrant cortical network activity, is a contributing factors to the neurological phenotypes found in DS. Taken together these results demonstrate that human stem cell derived cortical networks can serve as an ideal model system to study human cortical network development and function.