Transmembrane neuronal currents that embody cognition in the cortex produce magnetoencephalographic and electroencephalographic signals. Frequency-domain analysis reveals standard rhythms with consistent topography, frequency, and cognitive correlates. Time-domain analysis reveals average event-related potentials and field (ERP/ERF) components with consistent topography, latency, and cognitive correlates. Standard rhythms and ERP/ERF components underlie perceiving stimuli; evaluating whether stimuli match predictions, and taking appropriate action when they do not; encoding stimuli to permit semantic processing and then accessing lexical representations and assigning syntactic roles; maintaining information in primary memory; preparing to take an action; and closing processing of an event–response sequence. Sustained mental processes are associated with theta and gamma. Consolidating memories appears to occur mainly during replay of specific firing patterns during sleep spindles and slow oscillations. Biophysical, neuroanatomical, and neurophysiological factors interact to render cognitive rhythms and components particularly sensitive to the large-scale modulatory processes that sequence and integrate higher cortical processing.