Mixed-dimensional problems are of interest in such diverse fields as capillary networks and reinforced concrete. In these and several other situations, models of different dimensionality must be coupled to understand their joint behavior. This is complicated by the fact that the governing equations of systems of disparate dimensionality are posed over solution spaces that are widely different, and often incompatible. Several techniques have been proposed in recent years to address problems of mixed-dimensionality. The underlying problem that all these methods attempt to cope with is the lack of well-defined traces on low-dimensional manifolds of the problems posed on high-dimensional spaces. In this work, we will describe a recently proposed approach [Portillo, 2026] that employs the Arlequin method to coupled mixed-dimensional solids in structural problems. The formulation, valid both in the linear and nonlinear ranges, has provable stability in the linear regime. It can be employed to embed fibers, flat bodies, and rigid inclusions inside deformable bodies, with dramatic computational savings as compared to the detailed coupled solution. In the talk, we will describe the method, its theoretical foundations and showcase some of its applications to linear and nonlinear problems of solid mechanics.