With the proliferation of IoT devices and the continuous advancement of AI al- gorithms, edge AI, which represents the synergy of edge computing and artificial intelligence, has garnered increasing attention from both academia and industry. By pushing AI frontier to the edge ecosystem which is closer to users, edge AI provides substantial benefits such as low-latency inference, reduced network bandwidth us- age, and enhanced user privacy. However, deploying compute-intensive AI models on resource-constrained edge platforms presents substantial challenges to resource man- agement, which plays a key role in realizing the benefits and ensuring the success of edge systems. It is imperative to efficiently schedule and share the heterogeneous and limited edge resources, including emerging specialized AI accelerators such as GPUs and TPUs, to adapt to the dynamic edge workloads and satisfy their low-latency requirements. Additionally, energy, particularly for battery-powered edge devices, must be considered as a scarce resource, necessitating efficient operation to support the long-term execution of workloads. This thesis addresses pivotal challenges of resource management in Edge AI. By optimizing resource and energy efficiency for AI applications within the constraints of edge computing environments, this thesis aims to enhance hardware utilization, reduce costs, and improve application performance and reliability.