Design and structural optimization has become a very important field in industrial applications over the last years. Due to economical and ecological reasons, the efficient use of material is of highly industrial interest. Therefore, computational tools based on optimization theory have been developed and studied in the last decades. In this work, different structural optimization methods are considered. Special attention lies on the applicability to three-dimensional, large-scale, multiphysic problems, which arise from different areas of the industry. Based on the theory of PDE-constraint optimization, descent methods in structural optimization require knowledge of the (partial) derivatives with respect to shape or topology variations. Therefore, shape and topology sensitivity analysis is introduced and the connection between both sensitivities is given by the Topological-Shape Sensitivity Method. This method leads to a systematic procedure to compute the topological derivative by terms of the shape sensitivity. Due to the framework of moving boundaries in structural optimization, different interface tracking techniques are presented. If the topology of the domain is preserved during the optimization process, explicit interface tracking techniques, combined with mesh-deformation, are used to capture the interface. This techniques fit very well the requirements in classical shape optimization. Otherwise, an implicit representation of the interface is of advantage if the optimal topology is unknown. In this case, the level set method is combined with the concept of the topological derivative to deal with topological perturbation. The resulting methods are applied to different industrial problems. On the one hand, interface shape optimization for solid bodies subject to a transient heat-up phase governed by both linear elasticity and thermal stresses is considered. Therefore, the shape calculus is applied to coupled heat and elasticity problems and a generalized compliance objective function is studied. The resulting thermo-elastic shape optimization scheme is used for compliance reduction of realistic hotplates. On the other hand, structural optimization based on the topological derivative for three-dimensional elasticity problems is observed. In order to comply typical volume constraints, a one-shot augmented Lagrangian method is proposed. Additionally, a multiphase optimization approach based on mesh-refinement is used to reduce the computational costs and the method is illustrated by classical minimum compliance problems. Finally, the topology optimization algorithm is applied to aero-elastic problems and numerical results are presented.