The key to developing advanced materials is the understanding of the interplay between the various physical scales present, from the atomic level interactions, to the microstructural composition and the macroscale behavior. Rigorous mathematical and computational frameworks for multiscale and multiphysics modeling help to make super-lightweight, ultra-strength, low-wear and bio-inspired materials a reality of everyday life for energy related, industrial, and medical applications alike. In this presentation, advances in development of multiscale hybrid methods are reviewed, and then two novel approaches for the concurrent atomistic-continuum modelling of crystalline solids are demonstrated: the bridging scale projection method, and the domain reduction techniques (multiscale boundary conditions and the phonon heat bath). Issues of the hybrid modeling associated with the atomic scale plasticity, lattice dislocations, dispersive effects, and correlated thermal motion are paid a thorough attention. Discussion includes specific applications to nanoscale fracture of fcc materials, nanoindentation, and elastomechanics of carbon nanostructures.