With new multichannel recording technologies, neuroscientists can now record from cortex with high spatial and temporal resolution. Early recordings during anesthesia observed waves traveling across the cortex. While for a long time traveling waves were thought to disappear in awake animals, in recent work we have revealed spontaneous and stimulus-evoked traveling waves in these complex activity states. Their overall role in neural computation, however, remains poorly understood. In my research, we have introduced new, general computational methods for detection and quantification of spatiotemporal patterns in high-noise multielectrode recordings and imaging data. At the scale of a single cortical region, these methods have revealed that small visual stimuli consistently evoke waves traveling outward from the point of input in primary visual cortex of the awake monkey. At the whole-brain scale, the 11-15 Hz sleep "spindle", a brain oscillation causally implicated in consolidation of long-term memory, is consistently organized as a rotating wave traveling in a preferred direction. Our results indicate that traveling waves play a role in organizing neural activity during multiple behavioral states. In upcoming work, we aim to address the network-level mechanisms generating traveling waves and complex spatiotemporal patterns, under the general aim of understanding their functional roles in sensory processing and computation.