In this talk, we will highlight the development of numerical algorithms in the following areas where multiscale physical phenomena pose much challenges in  achieving computational efficiency. [1] Hybrid explicit/implicit solvation model  for long range electrostatic interactions in protein folding; [2] Adaptive conservative cell average spectral element methods of Wigner equations  for multi-physics models of electron transport in Nano-devices; [3] High frequency electromagnetic scattering in dispersive media in Phase shift Mask in nanoscale X-ray Lithography; [4] Modeling of contact and non-Newtonian  fluid mechanics with random rough surface in Chemical Mechanical Polishing (CMP) in VLSI chip design.