Low-dimensional semiconductors, such as quantum wells, wires, and dots, are recently finding wide applications in microelectronic and optoelectronic devices. In these semiconductor structures, the dimension is reduced to a scale of de Broglie wavelength. Electrons are confined to one dimension in a quantum well, two dimensions in quantum wire, and three dimensions in quantum dot. This chapter starts with some fundamental concepts and behavior of electrons in a low-dimensional quantum nanostructure. Electron energy levels and wave functions of three types of quantum wells are obtained from the solution of Schrödinger’s equation for square well, parabolic, and triangular potential functions. The energy levels and wave functions of electrons in quantum wire and dot are also obtained. The density of states functions for 2-D quantum well, 1-D quantum wire, and 0-D quantum dot are derived from delta function approach. Energy band structure of quantum well and excitonic confinement in the well are also presented in this chapter.