Hospital supply chain management (HSCM) is under pressure to adopt sustainable practices while balancing economic, social, and environmental factors. This systematic literature review explores the advancements, challenges, and future perspectives of sustainability in HSCM. By drawing on articles published between 2013 and 2023, the review identifies key themes such as the adoption of emerging technologies, the impact of socioeconomic changes, the need for resilience and risk management, and the potential of the circular economy. The analysis reveals a growing emphasis on social sustainability, which considers stakeholder perspectives and ethical considerations in supply chain decisions. Challenges include integrating sustainability into existing practices, balancing competing objectives, and measuring the impact of sustainable initiatives. Future research in HSCM should explore emerging technologies, social sustainability, post-pandemic resilience, and circular economy principles. By addressing these challenges and opportunities, stakeholders can contribute to a more sustainable and resilient healthcare system.