Coastal erosion describes the displacement of land caused by destructive sea waves, currents or tides. Due to the global climate change and associated phenomena such as melting polar ice caps and changing current patterns of the oceans, which result in rising sea levels or increased current velocities, the need for countermeasures is continuously increasing. Today, major efforts have been made to mitigate these effects using groins, breakwaters and various other structures. This thesis will find a novel approach to address this problem by applying shape optimization on the obstacles. Due to this reason, results of this thesis always contain the following three distinct aspects: The selected wave propagation model, i.e. the modeling of wave propagation towards the coastline, using various wave formulations, ranging from steady to unsteady descriptions, described from the Lagrangian or Eulerian viewpoint with all its specialties. More precisely, in the Eulerian setting is first a steady Helmholtz equation in the form of a scattering problem investigated and followed subsequently by shallow water equations, in classical form, equipped with porosity, sediment portability and further subtleties. Secondly, in a Lagrangian framework the Lagrangian shallow water equations form the center of interest. The chosen discretization, i.e. dependent on the nature and peculiarity of the constraining partial differential equation, we choose between finite elements in conjunction with a continuous Galerkin and discontinuous Galerkin method for investigations in the Eulerian description. In addition, the Lagrangian viewpoint offers itself for mesh-free, particle-based discretizations, where smoothed particle hydrodynamics are used. The method for shape optimization w.r.t. the obstacle’s shape over an appropriate cost function, constrained by the solution of the selected wave-propagation model. In this sense, we rely on a differentiate-then-discretize approach for free-form shape optimization in the Eulerian set-up, and reverse the order in Lagrangian computations.