Cohesive zone models (CZM) have been applied to a range of fracture and fatigue problems in the delamination of composites and the fracture of adhesive joints. Specific problems include the bridging of delamination cracks in composites and adhesive joints by oblique fibers, the influence of ductile materials in adhesive joints, and the bridging of cracks in the metal layers of fiber-metal hybrid laminates by intact composite plies. In all cases a non-linear traction law is applied to the crack faces in the wake of the crack tip. The resulting crack-tip stress intensity factor or strain energy release rate is equated to a fracture or fatigue crack growth criterion in order to predict crack propagation. Data is presented in the form of R-curves, load-displacement graphs or fatigue crack growth da/dN curves. In the present work the distinction is made between phenomenological and physically-based models, based on the degree of independent calibration and verification applied, which provides physically-based models with increased predictive capability, beyond the data set on which they were calibrated. A brief overview of the individual models is provided, and the physically-based and phenomenological approaches are compared and contrasted. 1