Synergistic integration of the Internet of Things (IoT), cloud computing, and big data technologies in healthcare have led to the notion of "smart health." Smart health is an emerging concept that refers to the provision of healthcare services for prevention, diagnosis, treatment, and follow-up management at any time or any place by connecting information technologies and healthcare. As a significant breakthrough in smart healthcare development, IoT-enabled smart devices allow medical centers to carry out preventive care, diagnosis, and treatment more competently. This review focuses on recently developed patient health monitoring platforms based on IoT-enabled smart devices that can collect real-time patient data and transfer information for assessment by healthcare providers, including doctors, hospitals, and clinics, or for self-management. We aimed to summarize the available information about recently approved devices and state-of-the-art developments through a comprehensive, systematic literature review. In this review, we also discuss possible future directions for the integration of cloud computing and blockchain, which may offer unprecedented breakthroughs in on-demand medical services. The combination of IoT with real-time, remote patient monitoring empowers patients to assert more control over their care, thereby allowing them to actively monitor their particular health conditions.