Nanostructures often possess unique properties, which may lead to the development of new microelectronic and optoelectronic devices. They also provide an opportunity to test fundamental quantum mechanical concepts such as the role of quantum confinement. Considerable effort has been made to understand the electronic and structural properties of nanostructures, but many fundamental issues remain. In this work, the electronic and structural properties of nanostructures are examined using several new computational methods. The effect of dimensional confinement on quantum levels is investigated for hydrogenated Ge <110> using the plane-wave density-functional-theory pseudopotential method. We present a real-space pseudopotential method for calculating the electronic structure of one-dimensional periodic systems such as nanowires. As an application of this method, we examine H-passivated Si nanowires. The band structure and heat of formation of the Si nanowires are presented and compared to plane wave methods. Our method is able to offer the same accuracy as the traditional plane wave methods, but offers a number of computational advantages such as the ability to handle large systems and a better ease of implementation for highly parallel platforms. Doping is important to many potential applications of nano-regime semiconductors. A series of first-principles studies are conducted on the P-doped Si <110> nanowires by the real-space pseudopotential methods. Nanowires of varied sizes and different doping positions are investigated. We calculate the binding energies of P atoms, band gaps of the wires, energetics of P atoms in different doping positions and core-level shift of P atoms. Defect wave functions of P atoms are also analyzed. In addition, we study the electronic properties of phosphorus-doped silicon <111> nanofilms using the real-space pseudopotential method. Nanofilms with varied sizes and different doping positions are investigated. We calculate the binding energies of P atoms, band gaps of the films, and energetics of P atoms in different doping positions. Quantum confinement effects are compared with P-doped Si nanocrystals and as well as nanowires. We simulate the nanofilm STM images with P defects in varied film depths, and make a comparison with the experimental measurement. / text