With the rapid growth of power market reform and power demand, the power transmission capacity of a power grid is approaching its limit and the secure and stable operation of power systems becomes increasingly important. In particular, in modern power grids, the proportion of dynamic loads with fast recovery characteristics such as air conditioners, refrigerators, and industrial motors is increasing. As well as there is an increasing proportion of different forms of renewable energy in power systems. Therefore, the short-term voltage stability (STVS) of power systems cannot be ignored. This article comprehensively sorts out the STVS problems of power systems from the perspective of data-driven methods and discusses existing challenges.