In line with the interests of the Special issue (SI) “Advanced mechanical Modeling of Nanomaterials and Nanostructures”, the present webinars will focus on the theoretical and numerical modeling of heterogeneous materials and enhanced structures, whose response could be affected by staking sequences, ply orientations, agglomeration of nanoparticles, volume fractions of the constituents and porosity levels. The series of talks will show different results from large numerical campaigns, focusing on fiber-reinforced composites and laminates, functionally graded materials, carbon nanotubes, graphene nanoplatelets, auxetic materials, latticed and cellular (honeycomb) materials, SMART constituents, together with innovative and advanced classes of composites such as Variable Angle-Tow laminates. Among many possible structural applications (e.g. SMART actuators, piezoelectric sensors, shape memory alloys, magnetostrictive and electrostrictive materials, or auxetic components), composite beams and shells with different geometries will be discussed, due to their unique shapes and outstanding mechanical behavior, accounting for their possible size-dependence. In a context where an increased computational demand is required to solve such complicated solid mechanics problems (including large deformation, crack propagation, high gradient, damage, vibration, or buckling problems), the webinar discusses about different high-performing computational strategies and advanced theoretical formulations, which are evaluated systematically against the available literature in their reliability and accuracy.