The theory of coupled phase oscillators provides a framework to understand the emergent properties of networks of neuronal oscillators. When the architecture of the network is dominated by short-range connections, the pattern of electrical output is predicted to correspond to traveling plane and rotating waves, in addition to synchronized output. We argue that this theory provides the foundation for understanding the traveling electrical waves that are observed across olfactory, visual, and visuomotor areas of cortex in a variety of species. The waves are typically present during periods outside of stimulation, while synchronous activity typically dominates in the presence of a strong stimulus. We suggest that the continuum of phase shifts during epochs with traveling waves provides a means to scan the incoming sensory stream for novel features. Experiments to test our theoretical approach are presented.