Design optimization has long played a crucial role in engineering, often with the goal of creating stiff and lightweight structures for aerospace and other applications. However, optimizing structures against failure is also crucial and has been less explored. Failure at interfaces is particularly challenging in design optimization as they involve high local stress concentrations and singular stresses. This dissertation demonstrates how mechanics models can be integrated with optimization schemes to engineer structures with improved interface adhesion and toughness. Finite element analysis is coupled with multiple optimization methods, including gradient and heuristic-based techniques, as well as machine learning-based approaches. It is shown that performance can be improved by formulating optimization schemes and objective functions based on the principles of mechanics and failure. First, optimal adhesive pillar geometries free from stress singularities are presented. Adhesion tests were performed, measuring a maximum adhesion enhancement of 2x. Second, optimal lap joint geometries are determined via changing the thickness of the adherend. The force-capacity was measured experimentally, with an enhancement of 2.4x over the standard geometry, achieved with aluminum joints. Then, the internal structure of a cellular adhesive joint is optimized via a perturbation-based optimization approach, shifting the defect initiation location from the edge towards the center. An adhesion enhancement of 2x was experimentally measured. Finally, tunable stiffness structures capable of manipulating stress distributions are investigated. From numerical calculations, the optimal distribution of stiffness that generates a uniform stress distribution with compressive stresses at the edge is determined. The versatility of the optimization schemes that have been developed enables them to be extended to other scenarios where performance can be improved by optimizing geometry and structure to control stresses.