The laser radiative cooling of electron beams via Thomson scattering is discussed, analyzed, and simulated. As a beam radiates via Thomson scattering, it is subsequently cooled, i.e., the mean energy, normalized energy spread, and normalized emittance are reduced in a similar manner. An analytical expression is derived for the damping distance, and this is found to agree well with electron beam transport simulations. Although laser cooling can occur rapidly (on ps time scales), it does not occur indefinitely, due to the effects of quantum excitation from discrete photon emission. Quantum excitation places serious limitations on the minimum energy spread and normalized emittance that can be obtained by laser cooling.