Energy limitations remain a key concern in the development of Internet of Medical Things (IoMT) devices since most of them have limited energy sources, mainly from batteries. Therefore, providing a sustainable and autonomous power supply is essential as it allows continuous energy sensing, flexible positioning, less human intervention, and easy maintenance. In the last few years, extensive investigations have been conducted to develop energy-autonomous systems for the IoMT by implementing energy-harvesting (EH) technologies as a feasible and economically practical alternative to batteries. To this end, various EH-solutions have been developed for wearables to enhance power extraction efficiency, such as integrating resonant energy extraction circuits such as SSHI, S-SSHI, and P-SSHI connected to common energy-storage units to maintain a stable output for charge loads. These circuits enable an increase in the harvested power by 174% compared to the SEH circuit. Although IoMT devices are becoming increasingly powerful and more affordable, some tasks, such as machine-learning algorithms, still require intensive computational resources, leading to higher energy consumption. Offloading computing-intensive tasks from resource-limited user devices to resource-rich fog or cloud layers can effectively address these issues and manage energy consumption. Reinforcement learning, in particular, employs the Q-algorithm, which is an efficient technique for hardware implementation, as well as offloading tasks from wearables to edge devices. For example, the lowest reported power consumption using FPGA technology is 37 mW. Furthermore, the communication cost from wearables to fog devices should not offset the energy savings gained from task migration. This paper provides a comprehensive review of joint energy-harvesting technologies and computation-offloading strategies for the IoMT. Moreover, power supply strategies for wearables, energy-storage techniques, and hardware implementation of the task migration were provided.