This article reviews the current literature on adaptive edge computing systems, focusing on design principles and research challenges. Edge computing brings computational resources closer to users to reduce latency and ensure quality of service. It is essential for edge-enabled smart systems that must handle dynamic environments with limited resources. Adaptation and self-organisation are crucial for maintaining performance in such systems. The article uses a widely accepted taxonomy to discuss aspects of adaptive behaviour, including adaptation reasons, levels of implementation, reaction time, adaptation techniques, and control. It identifies that most approaches target adaptation at the application level, with fewer focusing on middleware, communication infrastructure, and context. Reactive adaptation is common, though proactive adaptation is essential for maintaining performance and interoperability. Most approaches use centralised adaptation control, which may not fit the decentralised nature of edge computing. The article reviews various edge-enabled IoT applications, categorising them into smart infrastructure and smart services. It discusses the importance of adaptation in these applications and the challenges in implementing adaptive edge computing systems. The article highlights the need for self-adaptability and self-organisation in edge computing systems, especially in resource-constrained, dynamic environments. Self-adaptive systems can address these requirements by enabling components to change behaviour in response to environmental or system changes. These systems integrate self-* properties such as self-awareness, context-awareness, self-configuration, self-healing, self-optimisation, and self-protection. The article discusses the challenges in adapting edge computing systems, including the need for proactive adaptation, efficient resource management, and handling dynamic environments. It also highlights the importance of 5G networks in supporting edge computing applications with low latency and high throughput. The article concludes that self-adaptive systems are essential for ensuring the performance and reliability of edge computing systems in dynamic and uncertain environments.This article reviews the current literature on adaptive edge computing systems, focusing on design principles and research challenges. Edge computing brings computational resources closer to users to reduce latency and ensure quality of service. It is essential for edge-enabled smart systems that must handle dynamic environments with limited resources. Adaptation and self-organisation are crucial for maintaining performance in such systems. The article uses a widely accepted taxonomy to discuss aspects of adaptive behaviour, including adaptation reasons, levels of implementation, reaction time, adaptation techniques, and control. It identifies that most approaches target adaptation at the application level, with fewer focusing on middleware, communication infrastructure, and context. Reactive adaptation is common, though proactive adaptation is essential for maintaining performance and interoperability. Most approaches use centralised adaptation control, which may not fit the decentralised nature of edge computing. The article reviews various edge-enabled IoT applications, categorising them into smart infrastructure and smart services. It discusses the importance of adaptation in these applications and the challenges in implementing adaptive edge computing systems. The article highlights the need for self-adaptability and self-organisation in edge computing systems, especially in resource-constrained, dynamic environments. Self-adaptive systems can address these requirements by enabling components to change behaviour in response to environmental or system changes. These systems integrate self-* properties such as self-awareness, context-awareness, self-configuration, self-healing, self-optimisation, and self-protection. The article discusses the challenges in adapting edge computing systems, including the need for proactive adaptation, efficient resource management, and handling dynamic environments. It also highlights the importance of 5G networks in supporting edge computing applications with low latency and high throughput. The article concludes that self-adaptive systems are essential for ensuring the performance and reliability of edge computing systems in dynamic and uncertain environments.