Given the high attrition rate of de novo drug discovery and limited efficacy of single-agent therapies in cancer treatment, combination therapy prediction through in silico drug repurposing has risen as a time- and cost-effective alternative for identifying novel and potentially efficacious therapies for cancer. The purpose of this review is to provide an introduction to computational methods for cancer combination therapy prediction and to summarize recent studies that implement each of these methods. A systematic search of the PubMed database was performed, focusing on studies published within the past 10 years. Our search included reviews and articles of ongoing and retrospective studies. We prioritized articles with findings that suggest considerations for improving combination therapy prediction methods over providing a meta-analysis of all currently available cancer combination therapy prediction methods. Computational methods used for drug combination therapy prediction in cancer research include networks, regression-based machine learning, classifier machine learning models, and deep learning approaches. Each method class has its own advantages and disadvantages, so careful consideration is needed to determine the most suitable class when designing a combination therapy prediction method. Future directions to improve current combination therapy prediction technology include incorporation of disease pathobiology, drug characteristics, patient multiomics data, and drug-drug interactions to determine maximally efficacious and tolerable drug regimens for cancer. As computational methods improve in their capability to integrate patient, drug, and disease data, more comprehensive models can be developed to more accurately predict safe and efficacious combination drug therapies for cancer and other complex diseases.