Carrier confinement to reduced dimensions has recently become accessible to condensed matter experimentalists due to advances in microfabrication technology. The ability to create three- dimensionally confined structures, termed "quantum dots", has generated intensed interest in the investigation of artificially structured low dimensional systems. These structures are analogous to semiconductor atoms, with energy level tunable by the confining potentials. This proposal is aimed at a better understanding of the electronic transport in these systems and proposes a variety of novel structures to elucidate the relevant physics of low dimensional quantum transport.