Cognitive neuroscience is motivated by the precept that a discoverable correspondence exists between mental states and brain states. This precept seems to be supported by remarkable observations and conclusions derived from event-related potentials and functional imaging with humans and neurophysiology with behaving monkeys. This review evaluates specific conceptual and technical limits of claims of correspondence between neural events, overt behavior, and hypothesized covert processes examined using data on the neural control of saccadic eye movements.