Block copolymers (BCPs) consist of two or more chemically different polymers connected covalently, and are polymer alloys. Due to their thermodynamic incompatibility and chain connectivity, the phase separation between two (or more) blocks occurs only in a tens of nanometers range. Nanostructures are based on block copolymer self-assembly. They are functional nanomaterials less than 100nm in size and have received extensive scientific and technological attention due to their potential applications in electronic, biomedical, and optical materials. This chapter examines a variety of different synthetic strategies for preparation of linear diblock copolymers by anionic polymerization. Triblocks can be synthesized according to an appropriate synthetic pathway, depending on the monomers used and their sequence in the triblock chain. Nonlinear block copolymers including star block copolymers, graft copolymers, miktoarm star copolymers, cyclic block copolymers, and other complex architectures are explained. Microphase separation drives BCPs to self-assemble, resulting in ordered nanostructures, including spheres, cylinders, gyroids, and lamellae, depending on the composition of the BCP. In nanotechnology, self-assembly (SA) underlies various types of molecular structures built from nanoparticles, nanotubes, or nanorods. Supramolecular structures generated from amphiphilic block copolymers are characterized by a slow rate of intermicellar chain exchange which makes them interesting for a variety of applications. Basic principles of self-assembly and micellization of block copolymers in dilute solution, methods for stabilization of the macromolecular aggregates, are discussed. Stabilized nanoparticles, the so-called “smart materials,” which show responses to environmental changes (pH, temperature, ionic strength, etc.), are presented with a focus on their applications.