Flexible riser is a device which transports production fluids between floating vessels and subsea wells. With fewer remaining easy-to-access oil fields nowadays, flexible risers are being required to be installed in a water depth of over 3000m. However, the hydrostatic pressure at such a water depth may cause the collapse of flexible risers, and therefore predicting the critical collapse pressure is of great importance to their design. Riser collapse is a complex phenomenon related to material properties, geometry of the pipe and its overall surface topography and, therefore, makes the prediction of critical pressure challenging. Collapse prediction approaches of flexible risers have been developed for decades, yet a comprehensive review on their predictive capabilities, efficiency and drawbacks is lacking. In this paper, the recent advances on collapse studies of flexible risers are reviewed, which summarizes the methods developed for critical pressure prediction and highlights the related gaps in current research. This review aims to facilitate the current anti-collapse design and be a baseline for future utilization of flexible risers in deeper water expansion.