Ubiquitous sensors and smart devices from factories and communities guarantee massive amounts of data and ever-increasing computing power is driving the core of computation and services from the cloud to the edge of the network. As an important enabler broadly changing people’s lives, from face recognition to ambitious smart factories and cities, artificial intelligence (especially deep learning) applications and services have experienced a thriving development process. However, due to efficiency and latency issues, the current cloud computing service architecture hinders the vision of ‘providing artificial intelligence for every person and every organization at everywhere’. Thus, recently, a better solution is unleashing deep learning services from the cloud to the edge near to data sources. Therefore, edge intelligence, aiming to facilitate the deployment of deep learning services by edge computing, has received great attention. In addition, deep learning, as the main representative of artificial intelligence, can be integrated into edge computing frameworks to build intelligent edge for dynamic, adaptive edge maintenance and management. With regard to mutually benefited edge intelligence and intelligent edge, this paper introduces and discusses: 1) the application scenarios of both; 2) the practical implementation methods and enabling technologies, namely deep learning training and inference in the customized edge computing framework; 3) existing challenges and future trends of more pervasive and fine-grained intelligence. We believe that this survey can help readers to garner information scattered across the communication, networking, and deep learning, understand the connections between enabling technologies, and promotes further discussions on the fusion of edge intelligence and intelligent edge. Convergence of Edge Computing and Deep Learning: A Comprehensive Survey