Over the past 15 years, block copolymer lithography has emerged as its own research field within the broader block copolymer and polymer thin film communities. This distinction is associated with the unique requirements set by the semiconductor device industry, such as low-defect densities, precise feature registration, and complex pattern layouts. To achieve perfection in block copolymer lithography, the surface and substrate interactions must be carefully tuned to control domain ordering in three dimensions. This perspective discusses recent modeling efforts that underline the challenges of predicting interfacial interactions and the resulting block copolymer structures. We emphasize studies that facilitate the design and interpretation of experiments, including materials selection, guiding pattern geometry, and selecting tools for three-dimensional metrology. Finally, we propose that translation of block copolymer lithography to semiconductor manufacturing will require integrated experimental and modeling efforts to interrogate the vast parameter space that controls both lateral and out-of-plane ordering. (c) 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2015, 53, 96-102