The invention involves composite materials containing a polymer foam and an aerogel. The composite materials have improved thermal insulation ability, good acoustic insulation, and excellent physical mechanical properties. The composite materials can be used, for instance, for heat and acoustic insulation on aircraft, spacecraft, and maritime ships in place of currently used foam panels and other foam products. The materials of the invention can also be used in building construction with their combination of light weight, strength, elasticity, ability to be formed into desired shapes, and superior thermal and acoustic insulation power. The materials have also been found to have utility for storage of cryogens. A cryogenic liquid or gas, such as N2 or H2, adsorbs to the surfaces in aerogel particles. Thus, another embodiment of the invention provides a storage vessel for a cryogen.