Abstract Drug repositioning can drastically decrease the cost and duration taken by traditional drug research and development while avoiding the occurrence of unforeseen adverse events. With the rapid advancement of high-throughput technologies and the explosion of various biological data and medical data, computational drug repositioning methods have been appealing and powerful techniques to systematically identify potential drug-target interactions and drug-disease interactions. In this review, we first summarize the available biomedical data and public databases related to drugs, diseases and targets. Then, we discuss existing drug repositioning approaches and group them based on their underlying computational models consisting of classical machine learning, network propagation, matrix factorization and completion, and deep learning based models. We also comprehensively analyze common standard data sets and evaluation metrics used in drug repositioning, and give a brief comparison of various prediction methods on the gold standard data sets. Finally, we conclude our review with a brief discussion on challenges in computational drug repositioning, which includes the problem of reducing the noise and incompleteness of biomedical data, the ensemble of various computation drug repositioning methods, the importance of designing reliable negative samples selection methods, new techniques dealing with the data sparseness problem, the construction of large-scale and comprehensive benchmark data sets and the analysis and explanation of the underlying mechanisms of predicted interactions.