Quantum dots are artificially fabricated "atoms and molecules", in which charge carriers are confined in all three dimensions similar to the electrons in real atoms and molecules. Consequently, they exhibit similar properties normally associated with real atoms and molecules, such as quantized energy levels and shell structures. The detailed electronic structure of quantum dot systems depends on many of their physical properties such as material, size and geometry. Therefore, they can be readily engineered and manipulated to test fundamental concepts in quantum mechanics, to build more efficient and precisely controlled lasers and electronic devices, and to process vast amount of quantum information. This opens up a wide range of possibilities and areas for exploring new physics and new applications. In this paper, we present ab initio calculations on quantum dot systems by solving the corresponding Schrödinger's equations.