In materials systems there are a large number of situations in which uniform or random initial conditions are transformed into complex patterns. In many of these materials systems one of the competing forces driving the system to form patterns is the release of elastic stress. These stresses can arise due to remote loading applied to the system as a whole or due to residual stresses quenched into the material microstructure. I will present three examples of this overarching principle from my own theoretical and computational research studying the means by which materials react to stress. The first example is the complex variety of behaviors that can be exhibited near a crack tip during loading and dynamic fracture. These include blunting due to deformation near the crack tip and the possible injection of a dynamic crack into the solid. A dynamically propagating crack can lead to further patterns by branching. The second, related example is the development of localized deformation in otherwise homogeneous non-crystalline materials. These shear bands, as simulated using molecular dynamics methods, are comprised of alternating regions of tension and compression in the solid along the slip line. The final example is related to the process of three-dimensional islanding and pitting during the heteroepitaxial growth of III-V semiconductor thin films. Sequential nucleation events on the developing surface can lead to order that extends for many hundreds of microns. Such processes can potentially facilitate the growth of self-organized nanostructures. While each of these examples features stress interacting with a different competing mechanism (deformation, bond-breaking and diffusion) it is the complex nature of the relation between stress, structure and morphology that leads to the resulting complexity.