Edge Artificial Intelligence (Edge AI) and on-device machine learning represent significant advancements in computing paradigms, enabling real-time data processing directly at the edge of the network. This approach minimizes the need for centralized cloud-based processing, thereby reducing latency, enhancing privacy, and improving operational efficiency. This paper provides a comprehensive review of Edge AI and on-device machine learning, focusing on their applications, challenges, and future directions. Key applications include smart home devices, healthcare monitoring, autonomous vehicles, and smart city infrastructure, where local data processing facilitates immediate responses and decision-making. However, deploying AI models on edge devices introduces challenges related to model compression, limited computational resources, and power constraints. Security and privacy concerns also arise, necessitating robust data protection and privacy-preserving techniques. Furthermore, the paper explores emerging technologies such as 5G integration and advances in AI hardware, which are expected to drive future developments in Edge AI. Research directions are highlighted, emphasizing the need for new algorithms tailored to edge environments and enhancements in system robustness and reliability. By addressing these challenges and leveraging emerging technologies, Edge AI is poised to transform a wide range of sectors, offering enhanced real-time processing capabilities and paving the way for innovative applications.