Reduced-dimensional materials have attracted tremendous attention because of their new physics and exotic properties, which are of great interests for fundamental science. More importantly, the manipulation and engineering of matter on an atomic scale yield promising applications for many fields including nanoelectronics, nanobiotechnology, environments, and renewable energy. Because of the unusual quantum confinement and enhanced surface effect of reduced-dimensional materials, traditional empirical models suffer from necessary but unreliable parameters extracted from previously-studied bulk materials. In this sense, quantitative, parameter-free approaches are highly useful for understanding properties of reduced-dimensional materials and, furthermore, predicting their novel applications. The first-principles density functional theory (DFT) is proven to be a reliable and convenient tool. In particular, recent progress in many-body perturbation theory (MBPT) makes it possible to calculate excited-state properties, e.g., quasiparticle (QP) band gap and optical excitations, by the first-principles approach based on DFT. Therefore, during my PhD study, I employed first-principles calculations based on DFT and MBPT to systematically study fundamental properties of typical reduced-dimensional semiconductors, i.e., the electronic structure, phonons, and optical excitations of core-shell nanowires (NWs) and graphene-like two-dimensional (2D) structures of current interests. First, I present first-principles studies on how to engineer band alignments of nano-sized radial heterojunctions, Si/Ge core-shell NWs. Our calculation reveals that band offsets in these one-dimensional (1D) nanostructures can be tailored by applying axial strain or varying core-shell sizes. In particular, the valence band offset can be efficiently tuned across a wide range and even be diminished via applied strain. Two mechanisms contribute to this tuning of band offsets. Furthermore, varying the size of Si/Ge core-shell NWs and corresponding quantum confinement is shown to be efficient for modifying both valence and conduction band offsets simultaneously. Our proposed approaches to control band offsets in nano-sized heterojunctions may be of practical interest for nanoelectronic and photovoltaic applications. Additionally, I also studied the lattice vibrational modes of Si/Ge core-shell NWs. Our calculations show that the internal strain induced by the lattice mismatch between core and shell plays an important role in significantly shifting the frequency of characteristic optical modes of core-shell NWs. In particular, our simulation demonstrates that these frequency shifts can be detected by Raman-scattering experiments, giving rise to a convenient and nondestructive way to obtain structural information of core-shell materials. Meanwhile, another type of collective modes, the radial breathing modes (RBM), is identified in Si-core/Ge-shell NWs and their frequency dependence is explained by an elastic media model. Our studied vibrational modes and their frequency evolution are useful for thermoelectric applications based on core-shell nanostructures. Then I studied optical properties and exciton spectra of 2D semiconducting carbon structures. The energy spectra and wavefunctions of excitons in the 2D graphene derivatives, i.e., graphyne and graphane, are found to be strongly modified by quantum confinement, making them qualitatively different from the usual Rydberg series. However, their parity and optical selection rules are preserved. Thus a one-parameter hydrogenic model is applied to quantitatively explain the ab initio exciton spectra, and allows one to extrapolate the electron-hole binding energy from optical spectroscopies of 2D semiconductors without costly simulations. Meanwhile, our calculated optical absorption spectrum and enhanced spin singlet-triplet splitting project graphyne, an allotrope of graphene, as a good candidate for intriguing energy and biomedical applications. Lastly, we report first-principles results on electronic structures of 2D graphenelike system, i.e., silicene. For planar and simply buckled silicene structures, we confirm their zero-gap nature and show a significant renormalization of their Fermi velocity ix by including many-electron effects. However, the other two recently proposed silicene structures exhibit a finite band gap, indicating that they are gapped semiconductors instead of expected Dirac-fermion semimetals. This finite band gap of the latter two structures is preserved even with the Ag substrate included. The gap opening is explained by the symmetry breaking of the buckled structures. Moreover, our GW calculation reveals enhanced many-electron effects in these 2D structures. Finally the band gap of the latter two structures can be tuned in a wide range by applying strain.