Emotions are known to spread among people, a process known as emotion contagion. Both positive and negative emotions are believed to be contagious, but the mass spread of negative emotions has attracted the most attention due to its danger to society. The use of agent-based techniques to simulate emotion contagion in crowds has grown over the last decade and a range of contagion mechanisms and applications have been considered. With this review we aim to give a comprehensive overview of agent-based methods to implement emotion contagion in crowd simulations. We took a systematic approach and collected studies from Web of Science, Scopus, IEEE and ACM that propose agent-based models that include a process of emotion contagion in crowds. We classify the models in three categories based on the mechanism of emotion contagion and analyse the contagion mechanism, application and findings of the studies. Additionally, a broad overview is given of other agent characteristics that are commonly considered in the models. We conclude that there are fundamental theoretical differences among the mechanisms of emotion contagion that reflect a difference in view on the contagion process and its application, although findings from comparative studies are inconclusive. Further, while large theoretical progress has been made in recent years, empirical evaluation of the proposed models is lagging behind due to the complexity of reliably measuring emotions and context in large groups. We make several suggestions on a way forward regarding validation to eventually justify the application of models of emotion contagion in society.