Supporting seamless connection through user mobility is a critical challenge that must be addressed in mobile Heterogeneous Networks (HetNets). The case will become more worse in the future Ultra-Dense HetNets with the deployments of Fifth Generation (5G) and beyond mobile networks. That due to various key important factors, these factors include the use of Millimetre Waves (mmWaves), the massive growth of connected mobile equipment, overlapping network deployments, implementation of Dual Connectivity (DC), Carrier Aggregation (CA), emergence of connected drones, the massive deployment of small cells and the required for supporting high mobility speed scenarios. Consequently, this paper provides a comprehensive review of handover management in future mobile Ultra-Dense HetNets. Different mobility and handover management techniques are discussed to highlight their contribution in providing seamless connection during user mobility. Several key challenges, opportunities and prospective solutions are also examined to pinpoint key issues and determine suitable solutions that may contribute to solving mobility problems in future mobile networks. Conclusively, background studies and practical solutions are presented and discussed for future research directions.