Mortar methods have been introduced as a weak coupling strategy between subdomains with different scales, with nonconforming meshes, or between subproblems solved with different approximation methods. Despite the optimal error convergence obtained with the original elements, there are major numerical diffculties in applying this method to general 3D problems as encountered in real industrial applications. Such applications require some development of more flexible elements when dealing with general interfaces, a more refined analysis when dealing with large number of subdomains, extensions to handle nonlinear problems such as contact, or efficient numerical techniques to handle general nonlinear situations. This minisymposium addresses such issues.