This thesis explores the possibilities of design optimization techniques for designing shape memory alloy structures. Shape memory alloys are materials which, after deformation, can recover their initial shape when heated. This effect can be used for actuation. Emerging applications for shape memory alloys are e.g. miniaturized medical instruments with embedded actuation, as well as microsystem components. However, designing effective shape memory alloy structures is a challenging task, due to the complex material behavior and the close relationship between geometry, electrical, thermal and mechanical properties of the structure. In this thesis, various approaches are developed to combine optimization algorithms with computational modeling of shape memory alloy structures. The focus is on the shape memory behavior of NiTi alloys that exhibit the R-phase/austenite transformation. Dedicated computationally efficient constitutive models are formulated to capture this behavior and predict the performance of designs. The considered optimization approaches include deterministic shape optimization, shape optimization under bounded-but-unknown uncertainty, gradient-based shape optimization and topology optimization. Together they provide a collection of efficient and systematic techniques to generate well-performing designs. Their applicability and effectiveness is evaluated by application to design studies of realistic complexity, involving the design of miniature grippers and steerable catheters. The developed design optimization techniques are expected to be of great use for the design of future instruments and devices that utilize shape memory alloy actuation.