Ensuring reliable and stable communication during the movements of mobile users is one of the key issues in mobile networks. In the recent years, several studies have been conducted to address the issues related to Handover (HO) self-optimization in Heterogeneous Networks (HetNets) for Fourth Generation (4G) and Fifth Generation (5G) mobile networks. Various solutions have been developed to determine or estimating the optimum and ideal settings of Handover Control Parameters (HCPs), such as Time-To-Trigger (TTT) and Handover Margin (HOM). However, the complexity, high requirements, and the upcoming structure of ultra-dense HetNets require more advanced HO self-optimization techniques for future implementation. This paper studies HO self-optimization techniques that may implemented in the next-generation mobile HetNets by reviewing state-of-the-art algorithms. The solutions discussed in this survey are more focus on Mobility Robustness Optimization (MRO), which is a significant self-optimization function in 4G and 5G mobile networks. The applied solutions will preserve the continuous connection between the User Equipment (UE) and eNBs during UE mobility, thereby enhancing connection quality. The various algorithms and techniques applied to HO have revealed different outcomes. This paper discusses the pros and cons of these techniques, and further examines HO self-optimization challenges and solutions. New future directions for the implementation of HO self-optimization are also identified. This survey will contribute to the understanding of the issues related to mobility management, particularly in relation to the self-optimization of HO control parameters in future mobile HetNets.