There is significant potential for Operational Research to support improvements in care services for cancer patients. In this systematic review, we examine computer simulation techniques used in supporting hospital-based cancer care, the type of problems addressed, the quality of the model and implementation, and the impact on patients. We identified 51 papers distributed between four problem types: patient flow/pathway modelling, scheduling, cost analysis, and resource allocation. Discrete Event Simulation was the most common simulation technique. Nearly two-thirds of the papers involved some form of engagement with clinicians or hospital managers: studies that did not reported fewer successful implementations. We discuss the reported benefits and limitations of applying simulation techniques to cancer care. Papers often highlighted opportunities to reduce hospital costs or waiting times, while a common limitation was a lack of, or limited, data. Stakeholder involvement throughout the project may mitigate obstacles and result in lasting policy changes.