With the emergence of nanoscience, nanotechnology, and nanoengineering, a need for mathematical modeling of various materials and processes that take place at the nanoscale has been advanced. One "top-down" approach was to extend classical continuum models at macro and micro scales down to nanoscales. Another "bottom-up" approach was to extend standard discrete models at the atomic and molecular scales up to nanoscales. A compromise between the two, the so-called Internal Length Gradient (ILG) approach, was proposed by the author to generate both classical elasticity and plasticity continuum models, as well as atomistic and molecular dynamics models for interpreting nanoscale materials and processes. Among these central results concern the elimination of singularities that do not exist at the nanoscale, as well as the description of size effects that abandon at the nanoscale.