In 1929, at the dawn of quantum mechanics, Paul A. M. Dirac stated that the physical laws for a large part of physics and the whole of chemistry are completely known. The challenge is to develop practical methods for explaining the features of complex atomic systems. In this talk, we present a brief overview of some current theoretical and computational approaches employed in addressing Dirac’s challenge in the first-principles studies of materials and nanostructures. Some selected examples are given to illustrate the versatility of these methods and the underlying physics of the phenomena of interest.