The Internet of Medical Things (IoMT) has emerged as one of the most important key applications of IoT. IoMT makes the diagnosis and care more convenient and reliable with proven results. The paper presents the technology, open issues, and challenges of IoMT-based systems. It explores the various types of sensors and smart equipment based on IoMT and used for diagnosis and patient care. A comprehensive survey of early detection and postdetection care of the neural disorder dementia is conducted. The paper also presents a postdiagnosis dementia care model named “Demencare.” This model incorporates eight sensors capable of tracking the daily routine of dementia patient. The patients can be monitored locally by an edge computing device kept at their premises. The medical experts may also monitor the patients’ status for any deviation from normal behavior. IoMT enables better postdiagnosis care for neural disorders, like dementia and Alzheimer’s. The patient’s behavior and vital parameters are always available despite the remote location of the patients. The data of the patients may be classified, and new insights may be obtained to tackle patients in a better manner.