According to the neural efficiency hypothesis, brighter individuals might be characterized by lower and topographically more differentiated brain activation than less intelligent individuals, presumably reflecting a more specialized recruitment of task-related areas. The findings of several studies analyzing the event-related desynchronization (ERD) in the (upper) alpha frequency band have corroborated and elaborated the original neural efficiency hypothesis. In this chapter, we review classical and recent findings and argue in favor of a more differentiated picture of this phenomenon, emphasizing the role of participants' sex, task complexity, and material specificity, as well as the importance to select an adequate external criterion (intelligence measure). Also, recent ERD findings related to emotional intelligence and creativity as well as recent studies focusing on practice, learning ability, and expertise are presented, which point to the need of a broader neurophysiological ability concept. The reviewed findings point at the high suitability of the ERD method to uncover consistent and stable individual differences in people's brain activation patterns when engaged in performing cognitively demanding tasks.