A broad range of natural and man-made materials, such as the trabecular bone, aerogels have hierarchical microstructure. Performing efficient design of structures made from such materials requires the ability to integrate the governing equations of the respective physics on supports with complex geometry. The traditional approach is to devise constitutive equations which are either calibrated based on experiments or on micromechanics considerations. However, traditional homogenization cannot be used in most of these cases in which scale decoupling does not exist and the structure geometry lacks translational symmetry. Several efforts have been made recently to develop new formulations of mechanics that include information about the geometry in the governing equations. This new concept is based on the idea that the geometric complexity of the domain can be incorporated in the governing equations, rather than in the definition of the boundary conditions, as usual in classical continuum mechanics. In this chapter we review the progress made to date in this direction.