The rise of the Internet of Things (IoT) and Artificial Intelligence (AI) leads to the emergence of edge computing systems that push the training and deployment of AI to the edge of the network, so as to achieve reduced bandwidth cost, improved responsiveness, and better privacy protection. There exist several major limitations of existing research in edge computing for supporting AI applications at the edge. First, existing methods focus on a device-server offloading design while ignoring the collective computing power of privately owned devices. Second, the unique analytical skill and domain knowledge of the device owners (humans) are underutilized in existing edge computing systems. Third, the current centralized training of AI models is no longer appropriate in privacy-sensitive applications where the training data is owned by individuals. To address these knowledge gaps, the thesis proposes a new application paradigm, the social edge intelligence (SEI), that empowers intelligent applications at the edge by revolutionizing the computing, intelligence, and the training of the AI models. The integration of edge computing, humans, and AI in SEI allows machines and humans to make collaborative and optimized decisions that drastically improves the performance of edge-based intelligent applications. The SEI paradigm introduces a set of critical challenges such as pronounced heterogeneity of the edge devices, the resource limitation at the edge, and the privacy concern and rational nature of the human users. The thesis addresses these challenges by developing a series of principled algorithms and systems that enable the confluence of the computing capabilities of devices and the domain knowledge of the people, while explicitly addressing the unique concerns and constraints of humans. This thesis first develops a set of novel resource management frameworks that enable heterogeneous IoT devices owned by end-users to collaboratively provide computing power for executing AI models. The thesis then presents a human-machine interactive learning framework that leverages human intelligence to troubleshoot and improve the AI model performance. Finally, the thesis proposes several federated learning-based edge learning frameworks that allow device owners to contribute to the training of AI models with minimized privacy risks. The extensive evaluation of SEI in real-world edge computing applications shows that the proposed paradigm benefits edge intelligent applications by achieving impressive performance gains in various aspects such as service responsiveness, energy efficiency, model accuracy, and model fairness. SEI enables "social interactions" between machines and humans by allowing the edge devices to directly obtain the unique domain knowledge and expertise from humans to improve the performance and transparency of the application. SEI also gives rise to novel social good AI applications such as private-aware health monitoring, disaster damage assessment, and vehicle-based criminal tracking.