Diblock copolymer macromolecules may be viewed as giant amphiphiles. Such molecules readily self-assemble into a wide variety of structures which exhibit intermaterial dividing surfaces of approximately constant mean curvature. Order-disorder transitions in bulk materials result in ordered microdomain structures of BCC spheres, hexagonally packed cylinders and stacked lamella. An additional structure, the ordered bicontinuous double-diamond (OBDD) is also shown to occur as a cubic phase between the cylindrical and lamellar morphologies. The interface structure of the OBDD resembles a recently discovered family of constant mean curvature surfaces which include the Schwarz D minimal surface. Another interface structure which approximates Scherk's First Surface is a 90 twist boundary between grains of lamella. Blending of diblock copolymer with homopolymer provides a versatile binary system which displays a critical micelle concentration, spherical and cylindrical micelles, lamellar vesicles as well as ordering transitions depending on composition. The penetration of homopolymer into one side of the near-interface region accounts for the observed variations in interface curvature in blends from that of the pure diblock. Confining geometries, such as external surfaces, thin films and microdroplets can influence interface structures. Chaotic bicontinuous as well as parallel surface structures such as concentric spherical shells are shown to occur in microdroplets of a diblock copolymer which forms lamellar microdomains in the bulk