Improper management of medical waste poses significant ecological and public health risks, especially during epidemic outbreaks, such as the COVID-19 pandemic, where the volume of waste especially infectious waste increases dramatically. This paper offers a comprehensive review of medical waste management strategies, highlighting their role in mitigating environmental and health impacts. We examine the application of a variety of modeling techniques and solution approaches, including mathematical programming, system dynamics, forecasting models, and AI-based methodologies addressing both epidemic and non-epidemic conditions. The review discusses the modeling and solution applications of these approaches across different types of medical waste and their relevance to sustainability goals. It also explores critical variables and objectives that guide decision-making, such as waste reduction, recycling potential, and long-term environmental effects. By synthesizing existing research on planning horizons, decision-making frameworks, and regional case studies, this paper provides a roadmap for designing and implementing sustainable medical waste management systems. These insights are intended to help decision-makers in healthcare systems adopt strategies that not only optimize waste management efficiency but also promote sustainability in both crisis and non-crisis situations, paving the way for future research in the field.