We have investigated a variety of polymer systems containing block or graft copolymers in order to search for new classes of microphase-separated structures other than the ’classical morphologies’ such as lamellae, cylinders and spheres. The topological significance of these novel structures is that their interfaces have curvatures characteristic of hyperbolic surfaces. Systems exhibiting such structures can be divided into two groups : they are (a) polymer mixtures containing at least one block copolymer (e.g. block copolymer/homopolymer mixtures and block copolymer/block copolymer mixtures) and (b) block or graft copolymers with complex molecular architecture (e.g. star-block copolymers, graft-block copolymers, multicomponent multiblock copolymers, etc.).