Conventional planning of maintenance and renewal work for railway track is based on heuristics and simple scheduling. The railway industry is now collecting a large amount of data with the fast-paced development of sensor technologies. These data sets carry information about the conditions of various components in railway track. Since just before the beginning of the 21st century, data-driven models have been used in the predictive maintenance of railway track. This study presents a systematic literature review of data-driven models applied in the predictive maintenance of railway track. A taxonomy to classify the existing literature based on types of models and types of applications is provided. It is found that applying the deep learning methods, unsupervised methods, and ensemble methods are the new trends for predictive maintenance of railway track. Rail geometry irregularity, rail head defect, and missing rail components detection were the top three most commonly considered issues within the application of data-driven models. Prediction of rail breaks has received increasing attention in the last four years. Among these data-driven model applications, the collected data types are the most critical factors which affect selecting suitable models. Finally, this study discusses upcoming challenges in the predictive maintenance of railway track.