The Internet of Medical Things (IoMT) represents a transformative frontier in healthcare, enabling advancements in remote patient monitoring (RPM) and Hospital-at-Home (HaH) care. Central to realizing the potential of IoMT is effective device management (DM), encompassing provisioning, maintenance, firmware updates, and security assurance to ensure device reliability, interoperability, and regulatory compliance. This systematic review investigates the current academic landscape, challenges, and best practices in IoMT DM. Following PRISMA guidelines, 18 studies were identified, focusing on architectures, security, networking, and machine learning integration. Findings reveal the critical role of gateway architectures in addressing heterogeneity and enhancing data security while supporting edge computing capabilities. Despite progress in individual DM components, comprehensive solutions tailored to IoMT remain scarce. Emerging fields, including predictive maintenance using AI and software-defined networking (SDN), offer opportunities for future exploration. Challenges such as cybersecurity vulnerabilities, regulatory compliance, and managing device diversity highlight the need for standardized protocols and holistic DM frameworks. This review underscores the imperative to align technological innovation with regulatory demands to unlock the full potential of IoMT while safeguarding patient safety and data integrity.