It is widely recognized that further extension of optical lithography to even smaller dimensions will be accompanied by rapid increasing cost and difficulty. There is growing interest in devising alternative patterning methods that will support the evolution of microelectronics to the 10 nm length scale. Block copolymer lithography, which uses self-assembled microdomains of block copolymers in thin films, can provide arrays of periodic patterns of 10–50 nm length scales with a simple process and low cost. While this capability is attractive, the periodic nature of the microdomain patterns places significant restrictions on how block copolymer lithography can be practically implemented. In this review, the authors survey materials and methods for carrying out the controlled assembly of block copolymers in thin films for surface patterning applications. After a brief introduction to block copolymers and their phase behavior, the authors discuss ordering of block copolymer in thin films based on four different thickness categories. Approaches to directed self-assembly are reviewed along with the limitations and challenges of block copolymer lithography. Finally the authors note the circumstances that make it an opportune time to resolve the remaining technological issues facing block copolymer lithography and to demonstrate its utility as an adjunct to traditional photolithography.