We review research studies which use game theory to model the decision-making of individuals during an epidemic, attempting to classify the literature and identify the emerging trends in this field. The literature is classified based on (i) type of population modelling (classical or network-based), (ii) frequency of the game (non-repeated or repeated), and (iii) type of strategy adoption (self-learning or imitation). The choice of model is shown to depend on many factors such as the immunity to the disease, the strength of immunity conferred by the vaccine, the size of population and the level of mixing therein. We highlight that while early studies used classical compartmental modelling with self-learning games, in recent years, there is a substantial growth of network-based modelling with imitation games. The review indicates that game theory continues to be an effective tool to model decision-making by individuals with respect to intervention (vaccination or social distancing).