Abstract: As a vibrant and ever-evolving planet, the Earth has a dynamic evolution process spanning more than a dozen orders of magnitude from seconds (e.g., seismic rupture) to millions of years (e.g., mantle convection). Dynamic changes in underground media, spanning from minute to year scales, have been captured and analyzed based on seismic wave. This paper systematically summarizes the methods and applications of monitoring temporal changes of underground media based on seismic waves. We introduce traditional temporal variation monitoring methods like V_P/V_S ratio, shear wave splitting, coda Q value, and receiver functions, along with novel time-lapse seismic tomography. The new method focuses on repeated signals from active sources, repeat earthquakes, and ambient noise correlation, enhancing seismic velocity measurement accuracy via coda interferometry for underground medium monitoring. This paper also reviews key applications of seismic temporal changes monitoring, encompassing volcanic eruptions, earthquakes, landslides, industrial activities, slow earthquakes, core differential rotation, rainfall, as well as changes associated with environmental factors such as rainfall and groundwater levels. Lastly, future prospects for temporal variations of seismic velocity researches are anticipated in observation technology, data processing, and application domains.