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This thesis presents four investigations into mechanical aspects of soft thin structures, focusing on the effects of stochastic and thermal fluctuations and of material inhomogeneities. First, we study the self-organization of arrays of high-aspect ratio elastic micropillars into highly regular patterns via capillary forces. We develop a model of capillary mediated clustering of the micropillars, characterize the model using computer simulations, and quantitatively compare it to experimental realizations of the self-organized patterns. The extent of spatial regularity of the patterns depends on the interplay between cooperative enhancement and history-dependent stochastic disruption of order during the clustering process. Next, we investigate the influence of thermal fluctuations on the mechanics of homogeneous, elastic spherical shells. We show that thermal fluctuations give rise to temperature- and size-dependent corrections to shell theory predictions for the mechanical response of spherical shells. These corrections diverge as the ratio of shell radius to shell thickness becomes large, pointing to a drastic breakdown of classical shell theory due to thermal fluctuations for extremely thin shells. Finally, we present two studies of the mechanical properties of thin spherical shells with structural inhomogeneities in their walls. The first study investigates the effect of a localized reduction in shell thickness—a soft spot—whereas the second studies shells with a smoothly varying thickness. In both cases, the inhomogeneity significantly alters the response of the shell to a uniform external pressure, revealing new ways to control the strength and shape of initially spherical elastic capsules., Engineering and Applied Sciences