The composite shell of composite high pressure hydrogen storage vessel (CHPHSV) is the main structure in bearing inner pressure. Its failure will lead to leakage or burst of CHPHSV, which will cause serious safety problem and economic losses. So the security of CHPHSV has always been a key and difficult problem in academia and industry, which restricts the large-scale application of hydrogen. In this paper, the failures of composite shell of type III, type IV, and type V vessels are reviewed in experiment study, simulation method, optimization design, and damage detection, focusing on the burst modes (safe or unsafe), the influence of hydrogen-thermo-stress field, and the epistemic uncertainty. Firstly, the burst modes, failure behavior, test method, and influencing factors are summarized in the experiment study, and experiment for type V composite pressure vessel is discussed. Secondly, the simulation method is reviewed in the aspect of first ply failure (FPF) analysis and last ply failure (LPF) analysis. The damage evolution of safe burst mode and unsafe burst mode is summarized. Besides, the influence of hydrogen-thermo-stress field and the uncertainty characteristic are also reviewed. Moreover, simulations of micro-crack and permeability for type V composite pressure vessels are summarized. Then, the optimization design methods based on deterministic parameters and uncertain parameters are reviewed. Finally, the damage detection methods of the composite shell of CHPHSV are summarized. The experiment, numerical simulation, and optimization are important for design of the composite vessel, and the damage detection can significantly reduce the degree of uncertainty and maintenance safety. In the future research, precise model considering multiple damage modes, hydrogen-thermo-stress field effect should be established for simulation of safe and unsafe burst mode. Uncertain quantization should be studied for burst pressure with combination of stochastic uncertainty and epistemic uncertainty. Besides, the robust design method based on the reliability of CHPHSV considering the epistemic uncertainty of design parameters should be established for a larger safety margin.