Directed self-assembly (DSA) is a potentially promising method of writing lithographic patterns on a sub-40 nm length-scale. While the utility of DSA has been demonstrated in principle, there are many challenges that need to be solved before its wide adoption in the semiconductor industry. Computational modeling is crucial in addressing many of those challenges, for example, optimizing polymer formulations, producing a better pattern, or predicting the defect density. In particular, the use of mesoscale approaches such as Self-Consistent Field Theory (SCFT), coarse-grained Monte Carlo, coarse-grained Molecular Dynamics, and Dynamic Density Functional Theory (DDFT) to describe polymer morphologyboth bulk and in confinementis now widespread. These models are used to predict phase behavior of block copolymers in thin films (undirected self-assembly), as well as in cases of chemo- and graphoepitaxy (DSA). In the near future, modeling is expected to be an integral part of formulation design and screening process. (c) 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2015, 53, 90-95