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Nanostructures of semiconductor materials exhibit quantization effects when the electronic particles of these materials are confined by potential barriers to small regions of space. The confinement can be in one dimension producing quantum films, also termed quantum wells in the early 1980s as the first examples of quantization in nanoscale materials, in two dimensions (producing quantum wires or rods), or in three dimensions (producing quantum dots (QDs)). Some authors refer to these three regimes as 0D, 1D, or 2D, respectively, although these terms are not as precise. Nanostructures of other classes of materials, such as metals and organic materials, are also possible. Here, we will focus on semiconductor nanostructures and their potential applications to photovoltaics (PV). Nanostructures of crystalline materials are also referred to as nanocrystals; and this term includes a variety of shapes with the three types of spatial confinement, including spheres, cubes, rods, wires, tubes, tetrapods, ribbons, disks, and platelets. The first six shapes are being intensively studied for PV applications.