The formation of the Cenozoic N-S striking rifts in the Tibetan Plateau is the consequence of continuous contraction after the India-Asia collision. Its formation and evolution are of great significance for understanding the growth of the Tibetan Plateau. In recent years, geochronology, structural geology, geochemistry and geophysical exploration have been used to study the onset timing, mechanism and evolution process of the N-S striking rifts, and the N-S striking rifts are related to the deep dynamics in Tibet. However, it is still difficult to reach a consensus on the understanding of the N-S striking rifts in the Tibetan Plateau. This paper summarized the research status and existing problems on the onset timing, mechanism and their relationship with the deep layer of the plateau: the main extension period of the N-S striking rifts is Miocene; mechanisms controlling its formation are complex and may be various in different periods; the N-S striking rifts have a close genetic relationship with potassium and ultrapotassic rocks in the plateau, and their distribution may be affected by high-conductivity and low-velocity bodies. Based on existing knowledge, more precise geochronological constraints, deep process detection, and numerical modeling will be the future development trends in the study of N-S striking rifts.