Human blood is a scarce resource and its role in healthcare is fundamental, with donated blood saving the lives of many on a daily basis. The blood supply chain is responsible for the transfer of blood from donor to the recipient, but the availability of such an invaluable resource as human blood is ultimately attributable to the many voluntary donors. Thus, the efficiency of the collection of donated blood is crucial to the downstream effectiveness of the blood supply chain.We provide a detailed review on the use of quantitative methods for the process of blood collection from donors. We describe the functional areas which are appointment scheduling, collection policy, crisis situation, donor demographics, location/clinic planning, staff utilisation and vehicle routing. Furthermore, we analyse the existing literature with regards to methods, modelling objectives and the planning levels such as strategic, tactical and operational. Finally, we break down the articles into whether or not case studies lead to the implementation of the methods in practice. In total, we review 46 relevant publications on the intersection between OR/MS and other disciplines. We use our presented framework to categorise the existing approaches and highlight gaps such as scheduling of both staff and appointments for blood donation clinics.