Recent developments in block copolymer lithography suggest that triblock copolymers could enable fabrication of ultrasmall features over large areas. While the majority of past work with block copolymers has focused on diblocks, triblocks and multiblocks in general could offer distinct advantages for sublithographic patterning. In order to guide selection of appropriate materials and strategies, it is important to first determine the phase behavior that distinct molecular architectures exhibit in the bulk. Theoretically informed Monte Carlo simulations of a coarse grain model are used to predict the bulk morphologies of several linear triblock copolymers in three dimensions. Some of these triblocks are representative of the styrene-isoprene-methyl methacrylate system. The morphologies predicted by simulations, which incorporate fluctuation effects, are compared to those predicted by self-consistent field theory (SCFT). While the two approaches predict similar morphologies, some differences are identified when some of the blocks are short. We then consider several morphologies of lamellae forming triblock copolymer thin films on a patterned substrate, and use free energy calculations to determine the equilibrium states.