This review addresses a comparison, based on the literature, among nitrile rubber (NBR), ethylene-propylene-diene-monomer rubber (EPDM), and polyurethane (PU) elastomeric heat shielding materials (EHSM). Currently, these are utilized for the insulation of rocket engines to prevent catastrophic breakdown if combustion gases from propellant reaches the motor case. The objective of this review is to evaluate the performance of PU–EHSM, NBR–EHSM, and EPDM–EHSM as insulators, the latter being the current state of the art in solid rocket motor (SRM) internal insulation. From our review, PU–EHSM emerged as an alternative to EPDM–EHSM because of their easier processability and compatibility with composite propellant. With the appropriate reinforcement and concentration in the rubber, they could replace EPDM in certain applications such as rocket motors filled with composite propellant. A critical assessment and future trends are included. Rubber composites novelties as EHSM employs specialty fillers, such as carbon nanotubes, graphene, polyhedral oligosilsesquioxane (POSS), nanofibers, nanoparticles, and high-performance engineering polymers such as polyetherimide and polyphosphazenes.