Some mathematical models of physical phenomena can exhibit radically different behavior when modified slightly to account for additional physical mechanisms. This can be understood as fragility of the mathematical model to small "perturbations" in the dynamical description. These phenomena appear to be more ubiquitous than is generally believed. Hydrodynamic stability of wall-bounded shear flows is one striking example. The well-known phenomenon of Anderson localization is another one where small amounts of material disorder can radically alter the nature of dynamical modes. Recent work has shown that such localization phenomena can also occur without the presence of medium disorder, but rather due to complex geometry such as in vibrational modes of several naturally occurring enzymes. The common thread between these seemingly disparate phenomena is the fragility of eigenvalues/vectors of large-scale matrices and operators when perturbed in various ways. These observations inspire the search for similar fragilities in large-scale dynamical networks such as the power grid among others. This talk will weave this common thread between these seemingly disparate fields, and connect them to the area of robust control, which is concerned with the behavior of systems in the presence of unmodelled dynamics.