The purpose of drug repurposing is to leverage previously approved drugs for a particular disease indication and apply them to another disease. It can be seen as a faster and more cost-effective approach to drug discovery and a powerful tool for achieving precision medicine. In addition, drug repurposing can be used to identify therapeutic candidates for rare diseases and phenotypic conditions with limited information on disease biology. Machine learning and artificial intelligence (AI) methodologies have enabled the construction of effective, data-driven repurposing pipelines by integrating and analyzing large-scale biomedical data. Recent technological advances, especially in heterogeneous network mining and natural language processing, have opened up exciting new opportunities and analytical strategies for drug repurposing. In this review, we first introduce the challenges in repurposing approaches and highlight some success stories, including those during the COVID-19 pandemic. Next, we review some existing computational frameworks in the literature, organized on the basis of the type of biomedical input data analyzed and the computational algorithms involved. In conclusion, we outline some exciting new directions that drug repurposing research may take, as pioneered by the generative AI revolution.