Nanoscale polymer films have numerous potential applications such as protective coatings, flexible electronics, energy harvesting devices, and drug delivery systems. For realization of these potential applications, the mechanical properties of these materials and the underlying physics need to be understood. This dissertation focuses on understanding the responses of nanoscale films to mechanical deformations. In this regard, an elastic instability was exploited to locally bend and impart a local tensile stress in a nanoscale polystyrene film, and directly measure the resulting residual stress caused by the bending. Our results indicate that the onset of permanent deformation for thin polystyrene films is an order of magnitude smaller than what has been reported for the bulk value. In addition, not only is the onset of failure strain found to be small but also it increases with increased confinement. Using similar processing techniques, the yield strain of a more complex material - poly(styrene-b-divinylpyridine) - was studied. Similar to the polystyrene films, failure in polystyrene-b-poly(2-vinylpyridine) is also initiated at extremely low strain and is influenced by thin film confinement effects. In addition, we have demonstrated that internal nanostructure of self-assembled polystyreneb- poly(2-vinylpyridine) affects the onset of failure strain. Having introduced an idealized heterogeneity to a sample through ultraviolet/ozone treatment, we have created samples ranging from continuous thin films to sets of isolated plates. We demonstrated that, when subjected to mechanical deformation, the unbounded plates form isotropic undulations that persist even beyond high strain. In contrast, isolated plates undergo non-isotropic undulations in the range of high strains. The non-isotropic undulation shape has been described through a simple numerical modeling subjected to controlled boundary conditions. The agreement between experiment and numerical modeling is remarkable. Finally, through an integrated experimental methods and theoretical modeling, the response of discrete colloidal layers to mechanical deformations have been exploited. The buckling profiles measured experimentally demonstrate a great insight that the continuum model may not be able to predict the response of discrete systems. Theoretically, a granular model was constructed and structural stability analysis was investigated to predict the experimental observations. The overall agreement of the experiment and the modeling was good.