Flexible riser is a key enabler for the oil and gas production in ultra-deep water which transports production fluids between floating production systems and subsea wells. As oil and production heads to water depths in excess of 3000 m, high hydrostatic pressure has been one primary challenge facing the riser operators. Excessive hydrostatic pressure may cause collapse failure of flexible risers and thus predicting the critical collapse pressure is of significant importance to their anti-collapse design. Collapse is a complex phenomenon related to the material properties, the geometry of the pipe and its overall surface topography. Those factors make the prediction of critical pressure of flexible risers challenging. Related prediction approaches of collapse pressure of flexible risers have been developed for decades, yet a comprehensive review of their predictive capabilities, efficiency and drawbacks is lacking. This paper reviews the recent advances on collapse studies of flexible risers and highlights the gaps in existing prediction methods, aiming to facilitate the current anti-collapse design of flexible risers and provide a baseline for their future utilization in deeper water expansion.