Metaheuristic algorithms have emerged in recent years as effective computational tools for addressing complex optimization problems in many areas, including healthcare. These algorithms can efficiently search through large solution spaces and locate optimal or near-optimal responses to complex issues. Although metaheuristic algorithms are crucial, previous review studies have not thoroughly investigated their applications in key healthcare areas such as clinical diagnosis and monitoring, medical imaging and processing, healthcare operations and management, as well as public health and emergency response. Numerous studies also failed to highlight the common challenges faced by metaheuristics in these areas. This review thus offers a comprehensive understanding of metaheuristic algorithms in these domains, along with their challenges and future development. It focuses on specific challenges associated with data quality and quantity, privacy and security, the complexity of high-dimensional spaces, and interpretability. We also investigate the capacity of metaheuristics to tackle and mitigate these challenges efficiently. Metaheuristic algorithms have significantly contributed to clinical decision-making by optimizing treatment plans and resource allocation and improving patient outcomes, as demonstrated in the literature. Nevertheless, the improper utilization of metaheuristic algorithms may give rise to various complications within medicine and healthcare despite their numerous benefits. Primary concerns comprise the complexity of the algorithms employed, the challenge in understanding the outcomes, and ethical considerations concerning data confidentiality and the well-being of patients. Advanced metaheuristic algorithms can optimize the scheduling of maintenance for medical equipment, minimizing operational downtime and ensuring continuous access to critical resources.