The flourish of 5th generation wireless systems (5G) network has brought numerous benefits to the Internet of Things (IoT) with universal connectivity, improved data rate, and decreased latency. The development of IoT extends the computation-intensive applications from centralized servers to the edge of the network, promoting the paradigm of edge computing. Edge computing brings great assistance to IoT architecture by efficiently accomplishing tasks with lower latency, less energy consumption and reduced network bandwidth. Edge-assisted IoT emerges to provide location-aware services and offload computational tasks to edge nodes near the IoT devices. However, a series of security challenges still exist in edge-assisted IoT owing to the inherent vulnerabilities of edge nodes and sensitive nature of the collected data. Among the emerging and existing security schemes in IoT applications, security and energy consumption are two overriding yet conflicting requirements. The tradeoff between security and energy is critical to the sustainability of the IoT ecosystem but still lacks sufficient discussion. In this article, we investigate the security challenges in edge-assisted IoT and how the constraints in energy consumption can affect the design of security schemes. Specifically, we firstly present the architecture of edge-assisted IoT and its unique characteristics. Secondly, we identify the security threats in the edge-assisted IoT applications and the security-energy tradeoff during implementation. Thirdly, in a case study of distributed denial of service (DDoS) and malware injection attack, we propose a preliminary solution to address the conflict between security and energy requirements. Finally, we discuss some open issues and identify future research directions for security and energy efficiency in edge-assisted IoT.