To satisfy the high data demands in future cellular networks, an ultra-densification approach is introduced to shrink the coverage of base station (BS) and improve the frequency reuse. The gain in capacity is expected but at the expense of increased interference, frequent handovers (HOs), increased HO failure (HOF) rates, increased HO delays, increase in ping pong rate, high energy consumption, increased overheads due to frequent HO, high packet losses and bad user experience mostly in high-speed user equipment (UE) scenarios. This paper presents the general concepts of radio access mobility in cellular networks with possible challenges and current research focus. In this article, we provide an overview of HO management in longterm evolution (LTE) and 5G new radio (NR) to highlight the main differences in basic HO scenarios. A detailed literature survey on radio access mobility in LTE, heterogeneous networks (HetNets) and NR is provided. In addition, this paper suggests HO management challenges and enhancing techniques with a discussion on the key points that need to be considered in formulating an efficient HO scheme. INDEX TERMS Radio access mobility, cell selection, handover, LTE, 5G, NR, mobility enhancers. Ph.D. degree in electrical engineering with Aalto University, Finland. He has more than two years, from 2013 to 2015, of professional experience as an RF Planning and Optimization Executive at Wi-Tribe Pakistan Ltd. (Ooredoo Group). During his stay at KFUPM, he was associated with the King Abdullah University of Science and Technology (KAUST), Saudi Arabia, as a Visiting Student and a KFUPM-KAUST Joint Research Initiative. He has been a Researcher with the Helsinki Research Center, Huawei Technologies Finland Oy, since February 2018. His current research interest includes energy-efficient mobility for small-cell overlaid cellular networks. He received the Gold Medal Award for obtaining the first position in the B.Sc. degree. XAVIER GELABERT received the M.Sc. degree in electrical engineering from the KTH Royal Institute of Technology, Stockholm, in 2003, and the joint B.Sc. and M.Sc. degrees in telecom engineering and the Ph.D. degree (Hons.