The ability to stop ‒inhibit‒ ongoing responses that suddenly become inappropriate is essential for safe and effective interaction with an ever-changing and often unpredictable world. This ability is quantified by the stop-signal reaction time (SSRT), the completion time of an inhibitory process triggered by a signal to stop responding. Because SSRT cannot be directly observed, it must be inferred based on a model in which inhibitory (“stop”) and response (“go”) processes race with each other to control behavior. If the stop process wins the race, the response is inhibited; if the go process wins the race, the response is executed. Inhibitory control is usually studied in the context of choice responses, but there has been increasing recent interest in what is often a key component of skilled behavior, stopping a response that is timed to coincide with an anticipated event. I review the limitations of traditional non-parametric race models of response inhibition, such as the inability to account for attentional lapses and response accuracy, and the unrealistic assumption that the presentation of the stop signal does not affect the go process. These restrictions mean that the race model may not be used to investigate response inhibition in the full range of situations that are relevant to stopping in the real world. Here I present a Bayesian framework that addresses these shortcomings. I propose various parametrizations of the framework, ranging from the descriptive ex-Gaussian distribution to the racing Wald evidence-accumulation architecture, explore the strengths and weaknesses of the different models, and illustrate their utility with clinical and experimental data. The proposed modeling framework expands the scope of the race model to the study of response inhibition in the context of realistically difficult choices and provides a solid basis for the burgeoning study of timed-action control.