Neural mechanisms of cognitive control enable us to initiate, coordinate and update behaviour. Central to successful control is the ability to suppress actions that are no longer relevant or required. In this article, we review the contribution of cognitive neuroscience, molecular genetics and clinical investigations to understanding how response inhibition is mediated in the human brain. In Section 1, we consider insights into the neural basis of inhibitory control from the effects of neural interference, neural dysfunction, and drug addiction. In Section 2, we explore the functional specificity of inhibitory mechanisms among a range of related processes, including response selection, working memory, and attention. In Section 3, we focus on the contribution of response inhibition to understanding flexible behaviour, including the effects of learning and individual differences. Finally, in Section 4, we propose a series of technical and conceptual objectives for future studies addressing the neural basis of inhibition.