The central problem for cognitive neuroscience is to describe how cognitive processes arise from brain processes. This review summarizes the recent evidence that synchronous neural oscillations reveal much about the origin and nature of cognitive processes such as memory, attention and consciousness. Memory processes are most closely related to theta and gamma rhythms, whereas attention seems closely associated with alpha and gamma rhythms. Conscious awareness may arise from synchronous neural oscillations occurring globally throughout the brain rather than from the locally synchronous oscillations that occur when a sensory area encodes a stimulus. These associations between the dynamics of the brain and cognitive processes indicate progress towards a unified theory of brain and cognition.