The study of thermoelectric materials has recently been revived as an active research field, in part due to the recent demonstration of enhancement in the thermoelectric figure of merit of a two-dimensional (2D) PbTe quantum well system, relative to its three-dimensional (3D) bulk counterpart. Calculations suggest that the thermoelectric performance of any 3D material should show an enhanced thermoelectric figure of merit, when prepared as a 2D multi-quantum well superlattice, utilizing the enhanced density of states at the onset of each electronic subband, and the increased scattering of vibrational waves at the boundary between the quantum well and the adjacent barrier of the superlattice. In principle, low dimensionality also allows certain materials such as bismuth, which are poor thermoelectrics in 3D, to become good thermoelectrics. Thus, the successful fabrication of 1D bismuth nanowires offers new possibilities for the study of 1D systems for possible thermoelectric applications.