Abstract: The cohesive model as an effective tool is capable of analyzing the sizeeffect, progressive failure process, and the influence of the crack on concretestructures. Basic concept and definition of concrete cohesive model in thelight of fracture process zone (FPZ) are introduced. The commonmethods used for the softening characterization of the concrete are thensummarized, and they are primarily based on the following approaches: directtensile tests of notched samples, J-integral approach, fracture energy andtoughness, inverse approach, and $R$-curve method. As an application ofcohesive model, the cohesive failure modeling and simulation of concretebeams under Mode-I, mixed-mode, and fatigue loading are illustrated. Thesize effect based on concrete cohesive model is discussed.Comparisons of the cohesive model with other two models (i.e., crack zonestrip model and crack bridging model) are discussed in detail.Limitationsof cohesive model in engineering applications are pointed out, andthey may summarized as follows: (1) The cohesive model is primarily suitable for the crack underone dominant tensile stress; while the actual situation is under multiplestresses (e.g., the compressive stress may have an effect on cohesivefailure). (2) Most of cohesive model assumes that the crack line isstraight and the dissipation energy focuses near the crack tip. In fact,both the fracture surface (not necessarily along a straight crack line) andbase materials have a pronounced effect on the fracture energy and cohesivefailure. (3) Conventional cohesive model assumes that the nonlinearity(softening) only exists in the crack tip region where the stress reaches the limitingstress and the separation of material under tensile Mode-I loading occurs. Thus,the cohesive zone is referred to the area surrounding the crack tip, and thematerial outside this zone is taken as linear elastic. (4) Non-localbehavior of cohesive model should be considered. (5) Effect of nonlinearstress on cohesive model should be further studied. To promote research anddevelopment of the cohesive model in concrete, the following aspects shouldbe further investigated: (1) detection of crack initiation and softeningunder 3-D stresses; (2) mixed mode fracture mode under large sheardeformation; (3) time dependent behavior of crack propagation and relatedmaterial changes due to crack; (4) the stress-strain constitutive relationshipfor nonlinear base materials; (5) effects of cyclic loading historyand order, cyclic loading frequency and magnitude, size, and fatigue life onthe cohesive model.