98We review the dark/bright exciton model that describes the fine structure of the band-edge exciton in nanometer-size crystallites of direct-gap semiconductors with a cubic lattice structure or a hexagonal lattice structure, which can be described within the framework of a quasicubic model. The theory shows that the lowest energy exciton, which is eightfold degenerate in spherically symmetric nanocrystals (NCs), is split into five levels by the crystal shape asymmetry, the intrinsic crystal field (in hexagonal lattice structures), and the electron–hole exchange interaction. Two of the five states, including the ground state, are optically passive (dark excitons). The oscillator strengths of the other three levels (bright excitons) depend strongly on the NC size, shape, and energy band parameters. The state angular momentum projections on the crystal hexagonal axis (F = 0, ±1) determine polarization properties of the NC emission. An external magnetic field splits the levels and mixes the dark and bright excitons allowing the direct optical recombination of the dark exciton ground state. The developed theory is applied for description of various polarization properties of photoluminescence (PL) from CdSe NCs: the linear polarization memory effect, the polarization properties of single spherical and elongated (rod-like) NCs, the fine structure of the resonant PL, the Stokes shift of the PL, shortening of the radiative decay in a magnetic field, magnetocircular dichroism (MCD), and PL polarization in a strong magnetic field.