The most relevant issues related to headway variability in public transport planning, operations and quality of service are reviewed in this paper. We discuss the causes and consequences of headway variability, the alternative metrics that have been proposed to measure it, the preventive and reactive strategies to control headway variability in both research and practice, including the role of drivers and of present and future technology, and how service provision contracts might deal with headway variability through metrics and financial incentives. The most influential elements that explain headway variability along a route are the irregularity at which vehicles are dispatched, the scheduled frequency, the distance travelled or route length, the passenger demand and associated dwell times, and the number of stops. We conclude that there is a large gap between the state-of-the-art and the state-of-practice in terms of identification of headway variability issues, as well as in the development of mitigation and control measures. It is therefore paramount that future research will contribute to closing this gap by addressing organisational, contractual and technological barriers in the implementation of measures aimed at mitigating headway variability in public transport services.