Abstract: The seismic interferometric auto-correlation imaging method reconstructs virtual zero-offset reflection response beneath a single seismic station by stacking the auto-correlation of earthquakes or ambient noise. This technique has gained increasing attention for its capability to image Earth's interior structures, and has also been extended to studies of the Moon and the Mars. Relying solely on single-station records, it circumvents the need for inter-station synchronization and allows imaging using single component seismic data, enhancing operational flexibility. The auto-correlation imaging method, also known as the generalized receiver function or vertical receiver function, offers distinct advantages over conventional receiver functions. By utilizing frequency components with higher and broader-bandwidth from earthquakes or ambient noise, it achieves improved vertical resolution for imaging subsurface discontinuities. Moreover, it is less affected by multiple scattering phases, enhancing its robustness in complex geological environments. This method has been used to efficiently identify the major discontinuities in the Earth's interior, including the Moho, mid-lithospheric discontinuity, Hales discontinuity, lithosphere-asthenosphere boundary, and Lehmann discontinuity. In addition, it has been used to probe the anisotropy of the Earth's inner core. First, we briefly summarize the historical development of the auto-correlation imaging method. Second, we focus on its fundamental principles and processing workflows. Spectral whitening plays a key role in improving the auto-correlation imaging results. Phase-weighted stacking is a valuable procedure to enhance the signal-to-noise ratio and help to more easily identify weak yet important reflections with high coherence. Third, we outline recent advances in applications involving global, teleseismic, regional, and local earthquake events, as well as ambient noise in more detail. In the end, key challenges and potential solutions are discussed, and future directions are explored in the context of emerging trends in earthquake seismology.