Artificial intelligence (AI) technologies have emerged as pivotal enablers across a multitude of industries largely due to their significant resurgence over the past decade. The transformative power of AI is primarily derived from the utilization of deep neural networks (DNNs), which require extensive data for training and substantial computational resources for processing. Consequently, DNN models are typically trained and deployed on resource-rich cloud servers. However, due to potential latency issues associated with cloud communications, deep learning (DL) workflows are increasingly being transitioned to wireless edge networks in proximity to end-user devices (EUDs). This shift is designed to support latency-sensitive applications and has given rise to a new paradigm of edge AI, which will play a critical role in upcoming sixth-generation (6G) networks to support ubiquitous AI applications. Despite its considerable potential, edge AI faces substantial challenges, mostly due to the dichotomy between the resource limitations of wireless edge networks and the resource-intensive nature of DL. Specifically, the acquisition of large-scale data, as well as the training and inference processes of DNNs, can rapidly deplete the battery energy of EUDs. This necessitates an energy-conscious approach to edge AI to ensure both optimal and sustainable performance. In this paper, we present a contemporary survey on green edge AI. We commence by analyzing the principal energy consumption components of edge AI systems to identify the fundamental design principles of green edge AI. Guided by these principles, we then explore energy-efficient design methodologies for the three critical tasks in edge AI systems, including training data acquisition, edge training, and edge inference. Finally, we underscore potential future research directions to further enhance the energy efficiency of edge AI.