Block copolymers are ideally suited to prepare nanostructured materials. The phenomenon of microphase separation can lead to a variety of complex nanostructures of polymer materials for a wide range of applications. Foaming of block copolymers is a technique which allows one to prepare lightweight materials which are characterized by a low density, high acoustic and thermal insulation. Consequently, the use of block copolymers for foam processes is a promising approach to prepare multiscale structured polymer materials. Since foaming of polymers is strongly influenced by the rheological properties of the polymers, in this study we investigate the relation between rheological properties, processing and morphology of polymer foams based on block copolymers. In this work, different types of block copolymers were chosen for the preparation of polymer foams. In the first part, polystyrene-poly(methyl methacrylate) block copolymers were selected as model systems. Block copolymers with a cylindrical and a lamellar morphology with different molecular weights were chosen in order to investigate the influence of molecular architecture on the foam properties. The technique of batch foaming was applied to prepare the foams, and the blowing agent was carbon dioxide. Our experimental data indicate that block copolymers with a cylindrical morphology generally yield to foams with a lower density than block copolymers with a lamellar morphology. The cell walls of the block copolymers with a cylindrical morphology and a polystyrene matrix depicted the microphase-separated morphology with PMMA cylinders in a PS matrix. In the second part, the preparation of foams of polystyrene-polyisoprene (PS-PI) block copolymers will be discussed.