With the emergence of nanotechnology, the focus of materials research has shifted from bulk solids to nanoscale systems.  This emphasized the need for the development of simple and accurate theoretical methods capable of predicting the structural and electronic characteristics of nanomaterials.  Ab initio computational methods based on density functional theory (DFT) and time-dependent density functional theory (TDDFT) represent one of the primary theoretical tools for studying the properties of nanoscale structures.  However, the accuracy of DFT and TDDFT calculations strongly depends on the quality of the exchange-correlation functional.  In this colloquium, I will present the results of first-principles DFT and TDDFT calculations for the excitation energies, absorption spectra, and static electric dipole polarizabilities of atoms, molecules, and atomic clusters.  These calculations were carried out using several different representations of the exchange-correlation functional, including the local density approximation, generalized gradient approximation, and asymptotically correct Leeuwen-Baerends and Casida-Salahub potentials.  The results of these calculations suggest that the use of asymptotically correct exchange-correlation functionals can substantially improve the accuracy of the density functional formalism without a significant increase in computational cost.