Abstract There is a worldwide vision for providing high-quality healthcare services to patients. However, dealing with the growing number of patients and emergency situations poses several challenges on healthcare sector to maintain this vision. Thus, to cope with these challenges while providing the required scalability for healthcare systems, we present in this chapter our vision of leveraging edge computing within the field of smart health. Incorporating edge computing and advances of wireless networking technologies within the next-generation healthcare systems is one of the most promising approaches for enabling smart health services. Smart health systems give patients the opportunity to participate in their own treatment by providing them with intuitive, nonintrusive tools that allow them to be efficiently monitored and communicate with their caregivers. This chapter proposes a multiaccess edge computing (MEC) architecture, named s-Health, for enabling reliable and energy-efficient remote health monitoring. In particular, s-Health adopts data-specific and application-specific approaches for optimizing medical data delivery, leveraging edge processing and heterogeneous wireless networks. We envision that s-Health can have a significant impact on minimizing energy consumption, data delivery latency, and network bandwidth through mapping patient's context into different delivery modes. This chapter presents three main approaches that can be implemented at the s-Health architecture, namely, distributed in-network processing and resource optimization, event detection and adaptive compression, and dynamic networks association. The first approach optimizes medical data transmission from edge nodes to the healthcare providers, while considering energy efficiency and application's quality-of-service requirements. The second approach presents efficient data transfer scheme that maintains high reliability and fast emergency response using edge computing capabilities. The third approach leverages heterogeneous wireless network within the s-Health architecture to fulfill diverse applications' requirements while optimizing energy consumption and medical data delivery.