We present an in-depth analysis and benchmark of shape deformation techniques for their use in simulation-based design optimization scenarios. We first introduce classical free-form deformation, its direct manipulation variant, as well as deformations based on radial basis functions. We compare the techniques in a series of representative synthetic benchmarks, including computational performance, numerical robustness, quality of the deformation, adaptive refinement, as well as precision of constraint satisfaction. As an application-oriented benchmark we investigate the ability to adapt an existing volumetric simulation mesh according to an updated surface geometry, including unstructured tetrahedral, structured hexahedral, and arbitrary polyhedral example meshes. Finally, we provide a detailed assessment of the methods and give concrete advice on choosing a suitable technique for a given optimization scenario.