Current technology for decelerating a spacecraft from the high speed of atmospheric entry to the final stages of landing on Mars is based on low-density supersonic decelerators such as low mass and high packaging efficiency parachute systems. To enable future exploration missions featuring sophisticated robots and safely land heavier spacecraft on Mars, larger than before high-speed parachutes and inflatable drag devices are needed. The design, development, and maturing of such devices for future use at Mars require guidance from predictive simulations based on a high-fidelity, multi-disciplinary computational model for parachute inflation dynamics (PID) and drag prediction. The development of such a model is a formidable challenge. It must account for shocks, turbulence, and porous flow boundary conditions; the complexity of the behaviour of fabric material; massive contact between very thin surfaces; and highly nonlinear fluid-structure interactions in the presence of topological changes. The computational model must also be able to predict various instabilities of a parachute such as flutter and pulsation, the influence on its performance of several design factors including material and geometric porosities, and material failure. This lecture will discuss an ongoing effort at Stanford University, in collaboration with NASA Ames and the Jet Propulsion Laboratory, for the development of such a computational model and some associated computational innovations. These include: a multi-scale approach for modeling the dynamics of woven fabrics based on the concept of a locally attached microstructure and mechanics-informed machine learning; a discrete-event-free, spurious-oscillation-free, and total variation diminishing embedded boundary method for multi-material problems; a subgrid scale modeling approach for the treatment of porous wall boundary conditions; and an energy-conserving approach for the discretization of transmission conditions at the interface between fluid and structural representations of disparate spatial dimensions. The lecture will also report on validation results for the simulation of the supersonic inflation dynamics of: the parachute that landed Curiosity on Mars, on August 6, 2012; and those used in NASA’s 2018 ASPIRE tests to help decide which parachute design to use on the recent Mars 2020 mission that landed Perseverance on Mars, on February 18, 2021.