Abstract: Oblique transition is a transition scenario initiated by a pair of oblique waves with equal but opposite angles. It widely exists in boundary layer flow (over flat plate, cone at zero angle of attack, two-dimensional curved plate etc.), compression corner flow and free shear flow. Oblique transition/breakdown is not only one of the main natural transition paths in supersonic or hypersonic flows but also represents an important subcritical transition or bypass transition, which plays an important role in the transition of tube flow, channel flow and hypersonic large-blunt boundary (entropy) layer flows. Therefore, it is of great significance to carry out the study of oblique transition for comprehending the transition mechanisms, improving the transition prediction level, elevating the ability of the transition control, and ultimately optimizing the design of aircrafts. In this paper, important progress of studies on oblique transition in the past thirty years was reviewed, briefly introducing the physical mechanisms of oblique transition, its relationship with other transition scenarios and related control methods. Finally, some issues needed to be further studied were discussed.