This PhD project carries out research on the computational modeling and analysis of quantum dots. The main objectives are to model the electronic structure of the colloidal and self assembled quantum dots, and to quantify the quantum size effect (QSE) with respect to size, shape and material compositions. The various computational models such as effective mass approximation (EMA), finite width effective mass approximation (FWEMA), and finite element method (FEM) were explored. The FEM was found to be suitable for the numerical analysis of the transition energies of the electron and hole, and the stresses and strains in the quantum dots. In this work, two types of quantum dots are modeled, namely: self-assembled quantum dots and colloidal quantum dots. The structural properties such as strain and the strain-modified potential of the indium arsenide/gallium arsenide (InAs/GaAs) self-assembled quantum dots (SAQD) were obtained using the FEM and the k.p method. The electronic properties of the gold (Au), indium phosphate (InP), cadmium sulphide (CdS), zinc oxide (ZnO), copper chloride (CuCl), cadmium selenide (CdSe) colloidal quantum dots and indium arsenide/gallium arsenide (InAs/GaAs) self assembled quantum dots were studied by solving the single-particle EMA Schrödinger equation using the FEM.