The self-assembly of block copolymer thin films has attracted considerable attention as a promising high resolution lithographic tool due to its scale of microdomain ordering and its facility for modulation of both size and pattern. Our research has focused on developing improved block copolymer lithography techniques by means of self-consistent field theory (SCFT) simulations. We have demonstrated that directed self-assembly (DSA), which has already been shown to improve long-range ordering, can also be used to dictate the configuration and fidelity of the self-assembled structure. We demonstrate that lateral confinement combined with homopolymer additive can stabilize non-natural square arrays of microdomain ordering that are not found in pure block copolymer systems. Furthermore, we have shown that DSA can be used for high resolution VIA (Vertical Interconnect Access) lithography since it enhances the processing window through its reduced size variation and rectification properties. We also have developed a powerful suite of field-based computer simulation tools for exploring the self-assembly of complex polymeric fluids under confinement including a Chebyshev-based pseudo-spectral approach and a model that can incoporate deformable polymer/air interfaces. Finally, we have extended SCFT DSA techniques to mixed polymer brushes, in which dissimilar A and B chains phase separate on molecular length scales due to constraints imposed by having their ends grafted to a substrate. We identified the phase diagram of mixed brushes in the melt and demonstrated that lateral confinement and grafting density modulation can induce technologically attractive lateral phase separation for the application of self-assembled mixed polymer brushes in next-generation information storage and electronic devices.