Movement, cognition and perception arise from the collective activity of neurons within cortical circuits and across large-scale systems of the brain. While the causes of single neuron spikes have been understood for decades, the processes that support collective neural behavior in large-scale cortical systems are less clear and have been at times the subject of contention. Modeling large-scale brain activity with nonlinear dynamical systems theory allows the integration of experimental data from multiple modalities into a common framework that facilitates prediction, testing and possible refutation. This work reviews the core assumptions that underlie this computational approach, the methodological framework that fosters the translation of theory into the laboratory, and the emerging body of supporting evidence. While substantial challenges remain, evidence supports the view that collective, nonlinear dynamics are central to adaptive cortical activity. Likewise, aberrant dynamic processes appear to underlie a number of brain disorders.