Chronic cough is a significant problem, and in many patients cough remains refractive to both disease-specific therapies and current cough-suppressing medicines, creating a need for improved antitussive therapies. Most patients with chronic cough also display heightened sensitivity so that they experience a persistent sense of the need to cough, and often innocuous stimuli can trigger their coughing. This hypersensitivity underpins the newly described concept of cough hypersensitivity syndrome (CHS), a term that encapsulates the notion of common underlying mechanisms producing neuronal activation, sensitization and/or dysfunction, which are at the core of excessive coughing. Understanding these mechanisms has been a focus of recent research efforts in the field in the hope that new therapies can be developed to selectively target sensitized unproductive cough while maintaining the reflexive cough essential for airway protection. However, efforts to achieve this have been slower than expected, in part because of some significant challenges and limitations translating current cough models. In this review, we summarize recent advances in our understanding of the sensory circuits innervating the respiratory system that are important for cough, how cough sensory pathways become hypersensitive, and some of the recently described neural targets under development for treating chronic cough. We present the case that better use of current cough models or the development of new models, or both, is ultimately needed to advance our efforts to translate the discovery of basic cough mechanisms into effective medicines for treating patients with chronic cough.