Mobile applications can leverage high-quality deep learning models such as convolutional neural networks and deep neural networks to provide high-performance cognitive services. Prior work on deep learning models-based mobile applications in a cloud-edge computing environment focuses on performing lightweight data pre-processing tasks on edge servers for cloud-hosted cognitive servers. These approaches have two major limitations. First, it is uneasy for the mobile applications to assure satisfactory user experience in terms of network communication delay, because the intermediary edge servers are used only to pre-process data (e.g., images and videos) and the cloud servers are used to complete the tasks. Second, these approaches assume the pre-trained deep learning models deployed on cloud servers are static, and will not attempt to automatically upgrade in a context-aware manner. In this article, we propose a cloud-edge collaboration framework that facilitates delivering cognitive services with long-lasting, fast response, and high accuracy properties. We fist deploy a shallow model (i.e., EdgeCNN) on the edge server and a deep model (i.e., CloudCNN) on the cloud server. EdgeCNN can provide durable and rapid response cognitive services, because edge servers not only provide computing resources for mobile applications, but also close to users. Then, we enable CloudCNN to assist in training EdgeCNN to improve the performance of the latter. Thus, EdgeCNN also provides high-accuracy cognitive services. Furthermore, because users may continue to upload data to edge servers in real-world scenarios, we propose to use the ongoing assistance of CloudCNN to further improve the accuracy of the shallow model. Experimental results show that EdgeCNN can reduce the average response time of cognitive services by up to 55.08 percent and improve accuracy by up to 26.70 percent.