Motor symptoms of Parkinson's disease are related to the excessive synchronized oscillatory activity in the beta frequency band (around 20Hz) in the basal ganglia and other parts of the brain. This review explores the dynamics and potential mechanisms of these oscillations employing ideas and methods from nonlinear dynamics. We present extensive experimental documentation of the relevance of synchronized oscillations to motor behavior in Parkinson's disease, and we discuss the intermittent character of this synchronization. The reader is introduced to novel time-series analysis techniques aimed at the detection of the fine temporal structure of intermittent phase locking observed in the brains of parkinsonian patients. Modeling studies of brain networks are reviewed, which may describe the observed intermittent synchrony, and we discuss what these studies reveal about brain dynamics in Parkinson's disease. The parkinsonian brain appears to exist on the boundary between phase-locked and nonsynchronous dynamics. Such a situation may be beneficial in the healthy state, as it may allow for easy formation and dissociation of transient patterns of synchronous activity which are required for normal motor behavior. Dopaminergic degeneration in Parkinson's disease may shift the brain networks closer to this boundary, which would still permit some motor behavior while accounting for the associated motor deficits. Understanding the mechanisms of the intermittent synchrony in Parkinson's disease is also important for biomedical engineering since efficient control strategies for suppression of pathological synchrony through deep brain stimulation require knowledge of the dynamics of the processes subjected to control.