Use of data-driven methodologies in enhancing blood transfusion practices is rising, leveraging big data, machine learning, and optimization techniques to improve demand forecasting and supply chain management. This review used a narrative approach to identify, evaluate, and synthesize key studies that considered novel computational techniques for blood demand forecasting and inventory management through a search of PubMed and Web of Sciences databases for studies published from January 01, 2016, to March 30, 2023. The studies were analyzed for their utilization of various techniques, and their strengths, limitations, and areas for improvement. Seven key studies were identified. The studies focused on different blood components using various computational methods, such as regression, machine learning, hybrid models, and time series models, across different locations and time periods. Key variables used for demand forecasting were largely derived from electronic health record data, including clinical related predictors such as laboratory test results and hospital census by location. Each study offered unique strengths and valuable insights into the use of data-driven methods in blood bank management. Common limitations were unknown generalizability to other healthcare settings or blood components, need for field-specific performance measures, lack of ABO compatibility consideration, and ethical challenges in resource allocation. While data-driven research in blood demand forecasting and management has progressed, limitations persist and further exploration is needed. Understanding these innovative, interdisciplinary methods and their complexities can help refine inventory strategies and address healthcare challenges more effectively, leading to more robust, accurate models to enhance blood management across diverse healthcare scenarios.