Response inhibition is an essential aspect of cognitive control that is necessary for terminating inappropriate preplanned or ongoing responses. Response-selective stopping represents a complex form of response inhibition where only a subcomponent of a multicomponent action must be terminated. In this context, a substantial response delay emerges on unstopped effectors after the cued effector is successfully stopped. This response delay has been termed the stopping interference effect. Converging lines of evidence indicate that this effect results from a global response inhibition mechanism that is recruited regardless of the stopping context. However, behavioral observations reveal that the stopping interference effect may not always occur during selective stopping. This review summarizes the behavioral and neural signatures of response inhibition during selective stopping. An overview of selective stopping contexts and the stopping interference effect is provided. A “restart” model of selective stopping is expanded on in light of recent neurophysiological evidence of selective and nonselective response inhibition. Factors beyond overt action cancellation that contribute to the stopping interference effect are discussed. Finally, a pause-then-cancel model of action stopping is presented as a candidate framework to understand stopping interference during response-selective stopping. The extant literature indicates that stopping interference may result from both selective and nonselective response inhibition processes, which can be amplified or attenuated by response conflict, task familiarity, and functional coupling.