This manuscript summarizes a part of the work conducted since my doctoral thesis, as a CNRS junior researcher in the Laboratoire Jean Kuntzmann of Grenoble. It mainly revolves around the theme of numerical and applied shape and topology optimization, about which it embraces theoretical fundations as well as more practical aspects. After a fairly long introduction chapter, gathering basic material about optimal design and broaching perhaps less classical topics, the remainder of the document is decomposed into five chapters. Chapter 2 addresses the wish to make optimal designs robust with respect to the inevitable uncertainties plaguing the parameters of the physical situation; several formulations are proposed depending on the assumed knowledge about these uncertainties: worst-case design, stochastic approaches, and distributionally robust models. The next Chapter 3 is devoted to the modeling and incorporation of a few selected constraints raised by realistic applications of optimal design: after presenting a general-purpose constrained optimization algorithm, we notably consider constraints imposed by architectural applications, and by the recent additive manufacturing (a.k.a. 3d printing) processes. In Chapter 4, we investigate the interactions between the fields of asymptotic analysis and shape optimization. Notably, we leverage the classical topic of “small inhomogeneities” in the former field to construct original means to create variations of a domain – and thereby to optimize it: in this spirit, we consider the optimization of the regions bearing the boundary conditions of a physical model, and the optimization of a domain via the graft of a thin ligament. The next Chapter 5 proposes realistic applications of shape and topology optimization in quite original physical fields, such as fluid- structure interaction, nanophotonics, and quantum chemistry. A few broader perspectives for future research are eventually discussed in the final Chapter 6.