Finding new uses for existing drugs, or drug repositioning, has been used as a strategy for decades to get drugs to more patients. As the ability to measure molecules in high-throughput ways has improved over the past decade, it is logical that such data might be useful for enabling drug repositioning through computational methods. Many computational predictions for new indications have been borne out in cellular model systems, though extensive animal model and clinical trial-based validation are still pending. In this review, we show that computational methods for drug repositioning can be classified in two axes: drug based, where discovery initiates from the chemical perspective, or disease based, where discovery initiates from the clinical perspective of disease or its pathology. Newer algorithms for computational drug repositioning will likely span these two axes, will take advantage of newer types of molecular measurements, and will certainly play a role in reducing the global burden of disease.