Holographic near-eye displays can deliver realistic three-dimensional visual experiences, but their inherent space-bandwidth product leads to a trade-off between the eyebox and the field of view. An excessively small eyebox severely compromises the system's practical utility. In recent years, eyebox expansion techniques in holographic near-eye displays have attracted growing attention. To systematically review the research progress in this field, this paper started from the causes of eyebox constraints and provided a comprehensive review of existing methods for expanding the eyebox. First, the expansion techniques were categorized along multiple dimensions based on their underlying principles and implementation forms. Subsequently, a comparative analysis was conducted on the performance of various methods in terms of eyebox, field of view and reconstruction image quality(such as peak signal-to-noise ratio), summarizing their advantages, limitations and applicability. Finally, the challenges of current technologies were summarized, and future development trends were discussed.