The sixth generation (6G) networks represent the revolutionary processes in the field of wireless networks, such as ultra-dense network (UDN) frameworks, multi-dimensional connectivity, and network automation procured by AI. Nevertheless, the high rate of small cell and heterogeneous network environment proliferation poses severe challenges in handover management that result in higher signalling overhead, latency, and service interruptions. This review paper investigates the latest handover management solutions in 6G UDNs with some of the most significant challenges being mobility prediction, resource, and security constraints. We especially examine the new solutions, such as machine learning (ML)-based mobility prediction models, Long short-term memory (LSTM) and gated recurrent unit (GRU), reinforcement learning (RL)-based handover decision models, and split federated learning (SFL) of privacy-preserving optimization. Moreover, we will look at network-slicing integration and blockchain-based security solutions as an effort to ensure an efficient and dynamic handover procedure. The paper gives a methodological future study roadmap to optimisation of handover in ultra-dense 6G networks, which synthesizes existing approaches with research gaps identified. These results point to the necessity to optimise the interactions between layers and coordinate network efforts by using artificial intelligence and the proactive handover paradigm to provide seamless, low-latency, and energy-efficient mobility management in future next-generation wireless networks.