The self-assembly of classic diblock copolymers has been known to produce ordered mesophases at the nanoscale. Tailoring this self-assembly for engineering applications, however, requires more than relying on the natural behavior of these systems. The careful manipulation of the geometry and chemistry of surfaces can help guide diblock self-assembly into application relevant morphologies, leading to the potential for the use of block copolymers in nanolithography to produce semiconductor devices. Furthermore, the architecture of the polymer itself can be manipulated beyond the classic diblock to include multi-block and nonlinear motifs, leading to mesophases with larger domains and less regular structure. Such mesophases open the potential for extremely tough yet flexible thermoplastic elastomers. Using simulations, we probe key examples of these phenomena, including the use of diblock copolymers to pattern contact-hole morphologies for lithography and the critical influence of surface chemistry, the role of surface geometry and chemistry in determining the formation and annihilation of defects in line-and-space patterns for lithography, and the behavior of block copolymer thermoplastic elastomers formed from blends of star miktoarm copolymers and homopolymer assembled into the unique “bricks-and-mortar” mesophase.