In this thesis we investigate the relaxation mechanisms that occur in quantum dots (QDs). First we consider energy relaxation in single particle self-assembled QDs by means of an Auger process. For the first time, relaxation rates are compared for dots of a realistic truncated pyramid shape and for the more elementary dot models considered previously. We find that the fast (pico-second) relaxation necessary for quantum dot based optoelectronics applications is made possible by dot electrons scattering with electrons located in the surrounding bulk material. We show that this relaxation mechanism is dominant by two orders of magnitude over the two-dimensional wetting layer scattering mechanism that has been considered in previous calculations. Exact numerical diagonalisation is used to calculate the two-particle selfassembled QD wave functions. The small size of the QD means that the two electrons in the dot are found to be only weakly interacting. We find the relaxation rate for states of total spin 0 to be larger than the spin I rate by a factor of approximately 2. This is due to the double occupancy of the spin 0 spatial states. We also consider the much slower spin flip relaxation in electrostatic QDs. We include the spin-orbit mixing that results from the bulk inversion asymmetry of the crystal lattice in calculating the exact two-particle states. We find that the spin orbit mixing causes anti-crossings to appear in the energy spectrum and deduce a new conservation rule related to this. We find an oscillation capable of slowing the relaxation time from microseconds to tenths of a second. This oscillation results from the vertical finite well confinement of the QD. It is found to depend on both magnetic field and the QD thickness and is of particular interest for quantum information applications where long-lived excited states are desirable.