The bonded joints in composite structures is a challenging point in both research study and industry application.Compared with homogeneous and isotropic material, there is higher chance of stress concentration and intrinsic weak for this anisotropic structures. It is most common source of failure in structural laminates. So it is important to model and analyze the composite bonded joint to get the mechanical response and estimate the damage evolution. In this review paper, composite bonded joint are categorized based on bonded methods, materials, loading methods and failure modes. Multiple widely used adhesive bonded joint models including cohesive zone element model (CZM), interface element model, multiple point constraint model, kinking crack model, and repeating RVE model are introduced and discussed. To estimate the damage evolution in the bonded joint, a series of damage criteria have been developed including displacement based, stress based, energy based and modulus based damage criteria. Those damage criteria of bonded joint are also discussed and compared. This review work is important for the development of modeling of composite bonded joint in future.