There has been much recent progress in the synthesis and characterization of various nanostructures such as nanotubes, nanoscrystals, nanowires, organic and biological nanostructures. The progress in the basic and practical understanding, however, has been hampered by limitations in theoretical methods. The commonly used density functional methods, the most prominent theoretical tools for studying materials properties, severely underestimate excited state energies of semiconductors and insulators due to inaccurate energy functionals. On the numerical side, the poor scaling of numerical algorithms limit calculations to rather small systems. In this talk, Dr. Lee will describe recent efforts to overcome these problems by combining innovative developments in physics, numerical analysis, and massively parallel high performance computing. As for the excited states, he will show that the screened-exchange density functional method corrects the excited states problem in most semiconductor materials. For the scaling problem, Dr. Lee will present the newly developed Linear-Scaling 3-Dimensional Fragment method, which scales to thousands of processors. He also will present examples of his new methods, including electronic structures of calcium hexaborides and intrinsic electric dipole moments of CdSe nanorods, which are inaccessible with the conventional methods.