In order to reduce fuel consumption, lighter-weight materials such as aluminum alloys and carbon fiberreinforced plastics( CFRP) have been widely used in aircraft and automobile structures. These materialsdemand composite bonded joints as structural elements. Adhesive bonding has several advantages fromviewpoint of joint strength when compared with other mechanical joints. Therefore, it is important to estimatethe strength of these joints. The strengths of adhesive bonds are usually determined by destructive testswhich require trial and error procedure. In order to reduce time and cost estimating these joint strengths, thepractical evaluation method for these joint strengths using FEM has been desired. Recently, cohesive zonemodel( CZM) attracts special attention for prediction method of the strengths for bonding structures. In thepresent situation, the cohesive zone model has been installed in various FEM programs. Hence, CZM has beenwidely used for the strengths prediction of adhesive joints.In this review, the author overviewed an outline of cohesive zone model and its application for strengthprediction of adhesively bonded lap joints. In order to estimate the strength of the lap joints, the parametersof the CZM element under mode I and II conditions were necessary, which were determined from the DCB andENF tests in this case. Then, the strengths of the lap joints were estimated by using these parameters, whereinthe simulated fracture loads of the lap joints were well agreed with the experimental ones.In order to estimate the joint strengths with higher accuracy, it is necessary to clarify the fracture criterionsunder the mixed mode condition. Hence, in this review the several fracture toughness testing methods ofthe adhesive joints under mixed mode conditions were also described. The fracture loads of DCB and ENFtests were determined by crack growth simulation using cohesive element. It was found the relationship ofload-displacement curves showed good agreements with experimental results and analytical results. Thestrength of single-lap adhesive joints was estimated by FE analysis(FEA) using cohesive elements. Cohesiveparameters GIC and GIIC were obtained by DCB and ENF tests. The fracture load was calculated based on theconcept of a power law criterion as mixed-mode loading condition. The failure load predicted by FEA washigher than experimental result. The failure criterion must be identified by mixed-mode fracture toughnesstest. Finally, we conducted mixed-mode fracture toughness test of adhesive joints available for FEA usingcohesive element.