The demand for digital media services is increasing as the number of wireless subscriptions is growing exponentially.In order to meet this growing need,mobile wireless networks have been advanced at a tremendous pace over recent days.However,the centralized architecture of existing mobile networks,with limited capacity and range of bandwidth of the radio access network and low bandwidth back-haul network,can not handle the exponentially increasing mobile traffic.Recently,we have seen the growth of new mechanisms of data caching and delivery methods through intermediate caching servers.In this paper,we present a survey on recent advances in mobile edge computing and content caching,including caching insertion and expulsion policies,the behavior of the caching system,and caching optimization based on wireless networks.Some of the important open challenges in mobile edge computing with content caching are identified and discussed.We have also compared edge,fog and cloud computing in terms of delay.Readers of this paper will get a thorough understanding of recent advances in mobile edge computing and content caching in mobile wireless networks.