The concept of edge caching provision in emerging 5G and beyond mobile networks is a promising method to deal both with the traffic congestion problem in the core network, as well as reducing latency to access popular content. In that respect, end user demand for popular content can be satisfied by proactively caching it at the network edge, i.e., at close proximity to the users. In addition to model-based caching schemes, learning-based edge caching optimizations have recently attracted significant attention, and the aim hereafter is to capture these recent advances for both model-based and data-driven techniques in the area of proactive caching. This paper summarizes the utilization of deep learning for data caching in edge network. We first outline the typical research topics in content caching and formulate a taxonomy based on network hierarchical structure. Then, many key types of deep learning algorithms are presented, ranging from supervised learning to unsupervised learning, as well as reinforcement learning. Furthermore, a comparison of state-of-the-art literature is provided from the aspects of caching topics and deep learning methods. Finally, we discuss research challenges and future directions of applying deep learning for caching.