The integration of Edge Computing and Artificial Intelligence (AI) has revolutionized data processing and decision making by addressing challenges such as latency, bandwidth constraints, and privacy. By enabling computation near data sources, Edge Computing reduces latency and energy consumption while enhancing responsiveness. This paper presents a comprehensive survey of Edge AI, focusing on its applications, challenges, and future directions. Key domains include IoT, healthcare, autonomous systems, and cybersecurity. We also examine state-of-the-art approaches such as federated learning, model compression, and blockchain-based security. Finally, we discuss emerging directions including trustworthy and sustainable AI, and the convergence with 5G/6G technologies.