Abstract: Based on the demand of the third generation of advanced composites characterized by high strength, high toughness, high modulus and the balance of compressive and tensile strength, the development history of prediction model of continuous fiber reinforced polymer composite compressive strength was reviewed. The compressive failure mechanisms of continuous fiber reinforced polymer composites were discussed according to fiber microbuckling model, fiber kink-band model, combined model and progressive damage failure model. On the basis of the combined prediction model, the effects of carbon fiber (monofilament diameter, elastic modulus, volume fraction, initial deflection angle), polymer matrix (elastic modulus and shear modulus) and fiber/polymer interface on compressive strength and failure mode of continuous fiber reinforced polymer composite were investigated.