Novel cellular solids and foams from amorphous materials with a glass transition temperature (Tg) and methods of forming such materials are provided. In particular, foams are formed by expanding or compressing hollow spheres made of a high strength amorphous material, which is defined as a material having high strength characteristics, but also possessing a glass transition within a confined space. Using such a method, it has been unexpectedly found that it is possible to make cellular structures, including both open and closed cell foams, with customizable properties from materials that have been inaccessible with conventional methods. Moreover, based on calculations high specific strengths and stiffnesses are expected.