The polarization state of light is somewhat affected by propagation in a broad-spectrum, high numerical aperture (NA) and other optical systems with oblique incident angles. Changes in the polarization state, known as polarization aberrations, may result in severe deterioration of the imaging quality. This paper reviews the theory of polarization aberration, including the definition of polarization aberration, polarization ray tracing, analysis of the function of polarization aberration, and some new theories related to calculation and analysis procedures. Increasingly, the theory of polarization aberration has been analyzed and applied in optical systems such as interferometers, microscopes, telescopes, and lithography devices. In optical design, the combined calculation and simulation of a polarization aberration can contribute to the efficient optimization of optical system performance.