The blood supply chain (BSC) is a crucial and intricate system in the healthcare sector, which is marked by perishable products, fluctuating supply and demand, and a major impact of inefficiency. This paper showcases a detailed scientific review of BSC literature from 2010 to 2025 through scientometric methods, thereby mapping out its intellectual structure and development. By scrutinizing both foundational and recent publications, the authors are able to point out the research streams, methodological trends and main scholars. The scrutiny brings forward three leading research paradigms: (1) robust and resilient network design for disaster response, with Jawad as the leading scholar; (2) green and sustainable BSC modeling under uncertainty, where Pishvaee and his team are the main contributors; and (3) integrated inventory-routing problems for perishables, with Ramezanian as the pivotal author. This discipline is moving away from deterministic, single-objective models to the development of intricate multi-objective frameworks under hybrid uncertainties (robust, fuzzy, stochastic) which are being solved increasingly with metaheuristics and supported by case studies from real applications. The new trends include the combination of AI/ML for forecasting and decision-making, blockchain for transparency, and drones for the delivery part. The present review collects all these advancements and gives a succinct direction for both researchers and practitioners.