The stop-signal paradigm is very useful for the study of response inhibition. Stop-signal performance is typically described as a race between a go process, triggered by a go stimulus, and a stop process, triggered by the stop signal. Response inhibition depends on the relative finishing time of these two processes. Numerous studies have shown that the independent horse-race model of Logan and Cowan [Logan, G.D., Cowan, W.B., 1984. On the ability to inhibit thought and action: a theory of an act of control. Psychological Review 91, 295-327] accounts for the data very well. In the present article, we review the independent horse-race model and related models, such as the interactive horse-race model [Boucher, L., Palmeri, T.J., Logan, G.D., Schall, J.D., 2007. Inhibitory control in mind and brain: an interactive race model of countermanding saccades. Psychological Review 114, 376-397]. We present evidence that favors the independent horse-race model but also some evidence that challenges the model. We end with a discussion of recent models that elaborate the role of a stop process in inhibiting a response.