Internet of Things (IoT) enables different smart environment objects to communicate without involving humans. Recently, IoT has started a new challenge within the healthcare sector called the Internet of Medical Things (IoMT). The huge amounts of data generated by IoMT entities need to be analyzed in real-time to improve the performance and quality of service of the IoMT applications. Mobile Edge Computing-enabled 5G system is shown as a successful paradigm to address such an obstacle. Numerous frameworks are introduced in literature based on this idea. This paper presents a thorough discussion of MEC-based IoMT healthcare systems.