Block copolymers (BCPs) microphase-separate to form periodic patterns with periods of a few nanometers and above without the need for lithographic guidance. These self-assembled nanostructures have a variety of bulk geometries, including alternating lamellae, gyroids, arrays of cylinders or spheres, tiling patterns and core–shell structures, depending on the molecular architecture of the polymer and the volume fraction of its blocks. Non-bulk morphologies can be produced, the ordering of the microdomains can be improved, and their locations can be directed using various templates and processing strategies. The blocks themselves can constitute a functional material, such as a photonic crystal, or they can be used as a mask to pattern other functional materials, functionalized directly by various chemical approaches, or used as a scaffold to assemble nanoparticles or other nanostructures. BCPs offer tremendous flexibility in creating nanostructured materials with a range of applications in microelectronics, photovoltaics, filtration membranes, and other devices.