This thesis discusses two patterning techniques: Step and Flash Imprint Lithography, a nanoimprint technique, and patterning thin films utilizing electrohydrodynamic instabilities. Step and Flash Imprint Lithography, SFIL, is promising alternative approach to photolithography. SFIL replicates the relief pattern of a template in a photocurable liquid that has been dispensed on a substrate. The pattern is then crosslinked when the photocurable liquid is exposed to UV light through the template. In order to study the volume change in the created features upon exposure, a stochastic mesoscale model was formulated. This model allows the study of the possibility of defects forming, from under cured etch barrier, or particle contamination of the template. The results showed large defects should not occur regularly until the minimum feature size is below 3 nanometers. The mesoscale model proved to computationally intensive to simulate features of engineering interest. A base multiscale model was formulated to simulate the effects of the densification of the photocurable liquid as well as the effects of the polymerization on the feature integrity. The multiscale model combines a continuum model (compressible Mooney-Rivlin) coupled to the mesoscale code using the Arlequin method. The multiscale model lays the framework that may be adapted to the study of other SFIL processes like template release. Patterning thin films utilizing electrohydrodynamic instabilities allows for the creation of periodic arrays of pillar like features. These pillars form due to the electric field destabilizing the thin film. Prior work has focused on utilizing polymeric films heated above their glass transition temperatures. In order to decrease the process time in the pillar formation process, work was done to study photocurable systems. The systems which proved favorable to the pillar creation process were the thiol-ene system as well as the maleimide systems. Further work was done on controlling the packing and ordering of the formed pillar arrays by using patterned templates. The result of these studies is that control was only able to be achieved to the third generation of pillars formed due to the inability to fully control the gap over the entire active area. / text