This article reports on the physics-based models for the diagnosis (detection, isolation, localization, and quantification of damages) and prognosis (prediction of the future evolution of damages) of laminated composites. The model-based and data-driven prognostic strategies are compared, followed by a summary of the most common failure modes and the failure mechanisms of laminated composite materials. Then, an overview is provided of the measurement-based empirical/phenomenological and finite element-based damage evolution models for composite materials. The techniques reviewed in the former are Paris’s law and its modified versions, stiffness degradation models, Bayesian framework (Particle filters, Bayesian inference, dynamic Bayesian networks), and minimum strain energy theory. The finite element-based models overviewed failure criteria (Hashin, Puck, stress failure criteria) and damage propagation criteria (B-K criterion, equivalent strain/displacement criterion, strain rate-dependent damage model, cohesive zone modeling, De-Cohesive Law). Due to their complex failure modes, there is no generalized global solution for the diagnostics and prognostics of composite materials. The article will serve as guidelines for the physics-based prognostics and health management (PHM) of composite materials.