Doctor of Philosophy / Department of Physics / Talat S. Rahman / In this work we present a study of the geometric, electronic, vibrational and magnetic properties of several nanostructured systems for which experimental data call for a theoretical understanding. In order to investigate the effect of magnetic dipolar interactions on the magnetization of nanomagnets arranged in finite lattices, we utilize a phenomenological classical approach, which is based on the Landau-Lifshitz equation. Dipolar interactions lead to hysteretic behavior of the magnetization curves and established that the external field sweep rate, sample temperature, and shape anisotropy play a role in determining the specifics. Our results (derived from a classical approach) for magnets arranged in a square lattice suggest that stepped hysteresis curves do not have necessarily a quantum origin (quantum tunneling of the magnetization). We also find that in the square lattice small changes in the dipolar strength introduce sudden transitions in the magnetic hysteresis. For the examination of geometric vibrational and electronic structure of systems of interest, we turn to density functional theory (DFT), which is the leading technique for modeling nanoscale systems from first principles. We have applied DFT to either address some old queries of surface science, such as the dynamics of the CO-chemisorbed Cu(001) surface, or to contribute to the forefront of hydrogen-based economy through the comprehension of the growth and diffusion of Pt islets on Ru(0001), or to predict the geometric and electronic properties of materials to-be-created, as in the case of core-shell bimetallic nanoclusters. In the case of CO on Cu(001), although the bond has been considered to be weak enough so as to treat the adsorbate and substrate separately, our calculations are able to reproduce measurements and provide evidence that the dynamics of the molecule is influenced by the substrate and vice versa, as well as by intermolecular interactions. Taking into account the adsorbate-substrate interplay, has furthermore clarified issues that were pending for the clean surface and led to the correct interpretation of some features in the phonon dispersion of the chemisorbed surface. DFT has also directed us to the conclusion that the catalytic properties of few-atom Pt islets on Ru nanoclusters are preserved by the low probability of these islets to diffuse through the edges of the Ru nanoclusters. Moreover, the analysis of the Ag_{27}Cu_7 nanoalloy from ab initio methods has opened a wide panorama in terms of the geometry, coordination, energetics, and electronic structure of alloyed phases, in general,that may aid in the assembling on new materials.