To meet the increasing demand for patterning smaller feature sizes, a lithography technique is required with the ability to pattern sub-20 nm features. While top-down photolithography is approaching its limit in the continued drive to meet Moore's law, the use of directed self-assembly (DSA) of block copolymers (BCPs) offers a promising route to meet this challenge in achieving nanometre feature sizes. Recent developments in BCP lithography and in the DSA of BCPs are reviewed. While tremendous advances have been made in this field, there are still hurdles that need to be overcome to realize the full potential of BCPs and their actual use.