The demand for rich multimedia services over mobile networks has been soaring at a tremendous pace over recent years. However, due to the centralized architecture of current cellular networks, the wireless link capacity as well as the bandwidth of the radio access networks and the backhaul network cannot practically cope with the explosive growth in mobile traffic. Recently, we have observed the emergence of promising mobile content caching and delivery techniques, by which popular contents are cached in the intermediate servers (or middleboxes, gateways, or routers) so that demands from users for the same content can be accommodated easily without duplicate transmissions from remote servers; hence, redundant traffic can be significantly eliminated. In this article, we first study techniques related to caching in current mobile networks, and discuss potential techniques for caching in 5G mobile networks, including evolved packet core network caching and radio access network caching. A novel edge caching scheme based on the concept of content-centric networking or information-centric networking is proposed. Using trace-driven simulations, we evaluate the performance of the proposed scheme and validate the various advantages of the utilization of caching content in 5G mobile networks. Furthermore, we conclude the article by exploring new relevant opportunities and challenges.