The analysis, design, and development of planetary entry technologies rely heavily on computational modeling due to limited ground and flight test data, which simulate the extreme environments encountered by spacecraft during atmospheric entry. In general, these computational models possess uncertainties that may affect the prediction accuracy of the simulations. This makes uncertainty quantification a necessary tool for assessing the accuracy of model predictions and improving the robustness and reliability of entry systems. The objectives of this paper are twofold: to review uncertainty quantification studies applied to the modeling and simulation of planetary entry systems and to demonstrate an efficient uncertainty quantification approach based on stochastic expansions on the multidisciplinary analysis of a Hypersonic Inflatable Aerodynamic Decelerator configuration for Mars entry. The review of uncertainty quantification studies focuses on flight mechanics, guidance and navigation simulations, aerothermal modeling and prediction, fluid-structure interaction simulations, and thermal protection system response modeling of planetary entry technologies.