After a brief critical review of the basic arguments involved in the various interpretations of the mechanics on the material manifold and a short remark on the relationship of that approach with the late R. Stojanović's works, some of the recent advances in that field of continuum physics are presented. These include direct consequences in the numerics of solid-mechanics problems, general applications to the theories of plasticity, growth and mixtures, and a nonstandard application to the progress of phase- transition fronts in solids.