Clusters form a bridge between the atomic phase and the bulk phase. Due to their small sizes they display very interesting physical and chemical properties, which are different from their bulk counterparts. Their large surface-to-volume ratios brings out important surface effects and their confined nature leads to quantum confinement effects, both of which can be manipulated to control matter at the nano-scale and can lead to potential technological innovations. This thesis I presents results and analyses of my computations on the electronic and optical excitations in noble metal (Ag, Au, Cu) clusters and titania (TiO2) nanocrystals. I will model the ground state properties of these systems within the framework of density functional theory, and their excited states using two state-of-the-art computational formalisms, time-dependent density functional theory (TDDFT) and a many-body perturbation theory technique known as the GW-Bethe-Salpeter-Equation (GWBSE) method. Noble metal clusters are widely-studied systems due to their size-specific catalytic properties as well as their potential use in optoelectronic and plasmonic applications. They are also interesting due to the energetic and spatial proximity of their occupied d orbitals to the half-filled s orbital, which brings out important structural, electronic and optical properties. In the first part of my talk, I will present my first principles studies on Agn (n = 10 – 20) and Cun (n = 2 – 20) clusters with particular emphasis on the effects of the d electrons on their electronic and optical properties. I will also show that the first principles optical absorption spectra of these sub-nanometer sized clusters can be reproduced remarkably well within the framework of classical electromagnetism using the bulk dielectric functions of the metals. Titanium dioxide is arguably the most investigated singe-crystalline material in the field of surface science of metal oxides. Interest in this material arises from its numerous applications in catalysis, dye sensitized solar cells, and pigments, to name a few. In the second part of this thesis, I will present my results for the size and shape dependence of the electronic and optical excitations in bulk-terminated TiO2 nanocrystals. I will also show (similarly to the case of Ag and Cu clusters) that the absorption spectra of TiO2 nanocrystals (composed of 10 to 200 atoms) are dominated by surface plasmon peaks, and not by the van Hove singularities observed in the imaginary part of the bulk TiO2 dielectric function.