Composite pressure vessels (i.e. types III and IV) are widely used for compressed natural gas (CNG) vehicles, as storage cylinders to reduce the weight while maintaining high mechanical properties. These vessels can achieve 70-80% of weight saving, as compared to steel vessels (type I). So, prediction of first ply failure and burst pressure of these vessels is of great concern. Thus, this paper involved a review of literature regarding the first ply failure and burst pressure of composite pressure vessels (types III and IV). The review included the researches related to the simulation, mathematical modeling, and experimental analysis. The study focused on simulation-related research more than others due to the complexities of mathematical modeling of such problems in addition to the high cost of experimental tests. The results indicated that the stacking sequence of layers, vessel thickness and the type of selected composites were the main factors that mainly affect the vessel burst pressure performance. Accordingly, the optimization in the vessel structure (composite fabric architecture) parameters plays an important role in the performance of burst pressure. This in turn will lead to a high vessel durability, longer life-time and better prediction of burst pressure. Furthermore, the study showed that the prediction of first ply failure is more important than burst pressure knowledge of pressure vessels because it gives an initial prediction of vessel failure before the final failure occurrence. This in turn, may prevent the catastrophic damage of vessel.