This article reviews the current literature on adaptive edge computing systems, focusing on design principles and research challenges. Edge computing places computational services and resources closer to users to reduce latency and ensure quality of service. The article uses a widely accepted taxonomy to discuss aspects such as adaptation reasons, levels, time of reaction, techniques, and control of adaptive behavior. The analysis reveals that most approaches target application-level adaptation, with fewer focusing on middleware, communication infrastructure, and context. Reactive adaptation is prevalent, though proactive adaptation is essential for maintaining performance and interoperability. The article also highlights the need for decentralized adaptation control in edge computing settings. The research challenges and future directions in adaptive edge computing systems are discussed, emphasizing the importance of self-adaptability and self-organization in dynamic and resource-constrained environments.This article reviews the current literature on adaptive edge computing systems, focusing on design principles and research challenges. Edge computing places computational services and resources closer to users to reduce latency and ensure quality of service. The article uses a widely accepted taxonomy to discuss aspects such as adaptation reasons, levels, time of reaction, techniques, and control of adaptive behavior. The analysis reveals that most approaches target application-level adaptation, with fewer focusing on middleware, communication infrastructure, and context. Reactive adaptation is prevalent, though proactive adaptation is essential for maintaining performance and interoperability. The article also highlights the need for decentralized adaptation control in edge computing settings. The research challenges and future directions in adaptive edge computing systems are discussed, emphasizing the importance of self-adaptability and self-organization in dynamic and resource-constrained environments.