Future wireless networks provide research challenges with many fold increase of smart devices and the exponential growth in mobile data traffic. The advent of highly computational and real-time applications cause huge expansion in traffic volume. The emerging need to bring data closer to users and minimizing the traffic off the macrocell base station (MBS) introduces the use of caches at the edge of the networks. Storing most popular files at the edge of mobile edge networks (MENs) in user terminals (UTs) and small base stations (SBSs) caches is a promising approach to the challenges that face data-rich wireless networks. Caching at the mobile UT allows to obtain requested contents directly from its nearby UTs caches through the device-to- device (D2D) communication. In this survey article, solutions for mobile edge computing and caching challenges in terms of energy and latency are presented. Caching in MENs and comparisons between different caching techniques in MENs are presented. An illustration of the research in cache development for wireless networks that apply intelligent and learning techniques (ILTs) in a specific domain in their design is presented. We summarize the challenges that face the design of caching system in MENs. Finally, some future research directions are discussed for the development of cache placement and cache access and delivery in MENs.