<p>Composite materials are increasingly used in safety-critic structures, but their multiscale heterogeneity and complex damage mechanisms introduce significant uncertainty in model predictions. This survey reviews uncertainty quantification (UQ), uncertainty propagation, and finite element model updating (FEMU) for composite failure analysis, with emphasis on progressive damage modeling. The paper classifies key uncertainty sources (including material variability, manufacturing defects, model-form assumptions, and measurement noise) and compares deterministic, probabilistic, and non-probabilistic strategies for quantification and propagation. It also analyzes continuum and discrete damage models, highlighting their capabilities and limitations for describing matrix cracking, fiber failure, and delamination under uncertainty. In addition, the survey discusses deterministic and Bayesian FEMU workflows, surrogate-assisted approaches, and data-driven techniques used to reconcile simulations with experiments. Major research gaps are identified in benchmark standardization, scalable high-fidelity UQ, model-form uncertainty treatment, and integration with digital twin frameworks. The survey provides a structured reference and practical guidance for researchers and engineers developing uncertainty-aware composite damage and failure models.</p>