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This thesis describes studies of the growth and subsequent characterisation of wafers containing layers of Self-Assembled Quantum Dots grown by Molecular Beam Epitaxy (MBE). Insertion of such layers into transport structures is of particular interest for the creation of the new generation of optoelectronic devices. The growth of calibration structures containing InAs/GaAs Self-Assembled Quantum Dots is then outlined and certain growth parameters varied with the aim of tuning the emission energy and achieving narrow linewidths in the photoluminescence spectrum. Utilising the inherent non-uniformity of the Indium cell, which originates from the crucible design, we are able to achieve radial variations in the deposited thickness. Consequently, it has been possible to study the early stages of dot formation in some detail via the growth of uncapped samples for subsequent study using an Atomic Force Microscope (AFM). The properties of electrical devices containing a layer of InAs dots are discussed. In particular the mobility of an adjacent two-dimensional electron gas (2DEG) is strongly affected by the charge state of the dots themselves. In this structure it is possible to alter the charge state by either illumination, which removes charge from the dots, or by application of a positive gate voltage, which recharges the dots. After illumination the channel resistance drops significantly and persists for long timescales. This effect enables the creation of new types of optical memory or photon detector structures.