Atom transfer radical polymerization (ATRP) is the most extensively studied controlled/living radical polymerization (CRP) method, with the interest originating primarily in its simplicity and broad applicability, and in the ability to prepare previously inaccessible well-defined nanostructured polymeric materials. This review illustrates the range of well-defined advanced functional materials that can be prepared by ATRP. We detail the precise synthesis of macromolecules with predetermined molecular weight, designed molecular weight distribution, controlled topology, composition and functionality. The materials include polymers with site-specific functionalities and novel architectures that are starting to find commercial application--such as stars, bottle brushes, block and gradient copolymers. This is followed by discussing their self-assembly into materials with nanoscale morphologies. These macromolecular engineering procedures provide new avenues to nanostructured functional materials for many high-value applications, for example as thermoplastic elastomers, coatings, surfactants, dispersants and as optoelectronic and biomedical materials.