In this perspective, we survey recent advances in the synthesis and characterization of block copolymers, discuss several key materials opportunities enabled by block copolymers, and highlight some of the challenges that currently limit further realization of block copolymers in promising nanoscale applications. One significant challenge, especially as the complexity and functionality of designer macromolecules increases, is the requirement of multiple complementary techniques to fully characterize the resultant polymers and nanoscale materials. Thus, we highlight select characterization and theoretical methods and discuss how future advances can improve understanding of block copolymer systems. In particular, we consider the application of theoretical/simulation methods to the rationalization, and prediction, of observed experimental self-assembly phenomena. Finally, we explore several next steps for the field and emphasize some general areas of emerging research that could unlock additional opportunities for nanostructure-forming block copolymers in functional materials. In this perspective, we survey recent advances in the synthesis and characterization of block copolymers, discuss several key materials opportunities enabled by block copolymers, and highlight some of the challenges that currently limit further realization of block copolymers in promising nanoscale applications.