Methods for forming carbon-based cellular structures and 3D structures that can be formed by use of the methods are described. Methods include shaping an essentially 2D sheet that includes an organic polymer to form a 3D precursor followed by heat treatment of the 3D precursor. Heat treatment carbonizes the polymer to form an amorphous carbon. A metal precursor solution can be applied to the 3D precursor, and subsequent heat treatment can form a metal carbide, metal nanoparticles, or other carbon-based materials on/in the cellular structures.