With the rapid increase in the number of mobile users, wireless access technologies are evolving to provide mobile users with high data rates and support new applications that include both human and machine-type communications. Heterogeneous networks (HetNets), created by the joint installation of macro cells and a large number of densely deployed small cells, are considered an important solution to deal with the increasing network capacity demands and provide high coverage to wireless users in future fifth generation (5G) wireless networks. Due to the increasing complexity of network topology in 5G HetNets with the integration of many different base station types, in 5G architecture mobility management has many challenges. Intense deployment of small cells, along with many advantages it provides, brings important mobility management problems such as frequent handover (HO), HO failure, HO delays, ping-pong HO and high energy consumption which will result in lower user experience and heavy signal loads. In this paper, we provide a comprehensive study on the mobility management in 5G HetNet in terms of radio resource control, the initial access and registration procedure of the user equipment (UE) to the network, the paging procedure that provides the location of the UE within the network, connected mode mobility management schemes, beam level mobility and beam management. Besides, this paper addresses the challenges and suggest possible solutions for the 5G mobility management.