Response inhibition refers to an organism’s ability to suppress unwanted impulses, or actions and responses that are no longer required or have become inappropriate.In the stop-signal task, participants perform a response time task (go task), and occasionally, the go stimulus is followed by a stop signal after a variable delay, indicating subjects to withhold their response (stop task). The main interest of modeling is in estimating the unobservable latency of the stopping process as a characterization of the response inhibition mechanism. Here we analyze and compare the underlying assumptions of different models, including parametric and non-parametric versions of the race model. New model classes based on the concept of copulas are introduced and a number of unsolved problems facing all existing models are pointed out.