Flexible and stretchable supercapacitors are made using carbon nanostructures produced by providing a first composite structure which includes a temporary substrate and an array of carbon nanotubes arranged in a stack on a surface of the temporary substrate such that the stack of carbon nanotubes is oriented generally perpendicular to the surface of the temporary substrate, which may include silicon dioxide. The stack of carbon nanotubes is transferred from the temporary substrate to another substrate, which includes a curable polymer, thereby forming another composite structure comprising the stack of carbon nanotubes and the cured polymer.