Abstract: The failure behavior of fiber-reinforced laminated composites is often accompanied by complex damage mechanisms and by characteristic manifestations. An in-depth exploration of the strength properties and of damage evolution of such composites is of paramount importance for ensuring the service life of engineering structures, for optimizing research and development costs, and for advancing lightweight design and residual strength assessment of industrial products. Addressing the anisotropy of composites within the current framework of Peridynamics (PD) primarily involves two typical strategies: firstly, constructing bond pair models with different stiffness characteristics based on the physical property differences between constituent materials such as carbon fiber bundles and resin matrices; secondly, incorporating the anisotropic properties of composites into the elastic matrix to derive stress-strain constitutive relationships. However, most existing models focus on the linear elastic response of composites during the initial loading stage, while the exploration of key mechanical features remains insufficient, i.e., the insufficient exploration of shear nonlinearity, of stiffness degradation, and of large deformation characteristics exhibited during the damage progression stage. Furthermore, current research in PD primarily concentrates on the tensile and compressive properties of composites, with a relative lack of analysis on their bending, torsion, and tension-compression-bending-torsion coupling behaviors under out-of-plane loads. In light of this, this study first provides an overview of the fundamentals of continuous damage mechanics for composites, aiming to offer essential background knowledge and theoretical foundations for researchers in related fields. Subsequently, it systematically reviews the PD models applicable to composites, summarizing the current research progress and theoretical characteristics. Finally, discussed is the technical challenges faced by PD in practical engineering applications and, presented is the prospects for future research directions, with the intention of providing valuable insights for enhancing the understanding and engineering application of composite failure mechanisms.