The coupled task scheduling problem concerns scheduling a set of jobs, each with at least two tasks and there is an exact delay period between two consecutive tasks, on a set of machines to optimize a performance criterion. While research on the problem dates back to the 1980s, interests in the computational complexity of variants of the problem and solution methodologies have been evolving in the past few years. This motivates us to present an up-to-date and comprehensive literature review on the topic. Aiming to provide a complete road map for future research on the coupled task scheduling problem, we discuss all the relevant studies and potential research opportunities. In addition, we propose several sets of benchmark instances for the problem in various settings and provide a detailed evaluation of all the available models with a view to facilitating future research on the solution methods.