Fluid--structure interaction (FSI) modeling of spacecraft parachutes involves a number of computational challenges. The canopy complexity created by the hundreds of gaps and slits and design-related modification of that geometric porosity by removal of some of the sails and panels are among the formidable challenges. Disreefing from one stage to another when the parachute is used in multiple stages is another formidable challenge. This thesis addresses the computational challenges involved in disreefing of spacecraft parachutes and fully-open and reefed stages of the parachutes with modified geometric porosity. The special techniques developed to address these challenges are described and the FSI computations are be reported. The thesis also addresses the modeling and computation challenges involved in very early stages, where the sudden separation of a cover jettisoned to the spacecraft wake needs to be modeled. Higher-order temporal representations used in modeling the separation motion are described, and the computed separation and wake-induced forces acting on the cover are reported.