As an important hub equipment in the power system, the power transformer has increasingly higher requirements for its reliability and safety with the rapid development of the power industry. However, the vibrations and noise generated during its operation not only cause a series of issues such as loose windings, core wear, and fatigue of fasteners, but also lead to anxiety and unease among nearby residents, severely affecting their physical and mental health. Therefore, the generation mechanism and control measures of vibration and noise in power transformers have attracted extensive attention from scholars. The magnetostrictive effect of silicon steel sheets is one of the important factors in the causes of transformer vibration and noise. This paper focuses on the magnetostrictive effect of silicon steel sheets. Firstly, the micro mechanism of magnetostriction is introduced. Secondly, based on current research status, the vibration and noise mechanism caused by magnetostriction are summarized, and the influencing factors, measurement, modeling, and noise reduction methods based on magnetostriction are summarized. Finally, based on the current research status and future development trends, prospects are proposed, aiming to provide references for subsequent research on transformer vibration and noise.