This review paper describes the evolution of the quantification procedure for compositional depth profiling (CDP) in glow discharge optical emission spectrometry (GD-OES), based on the constant emission yield concept. The concept of emission yield (EY) is defined and ways of measuring it experimentally are discussed. The history of the development of quantitative CDP is reviewed, which shows that all of the different approaches depend on the assumption that the EY is essentially a matrix-independent quantity. Particular emphasis is placed on the dependence of the EY on the plasma parameters of current, voltage, power and pressure. In short, impedance changes (current voltage) can significantly affect the emission yield and should either be corrected mathematically or the impedance should be kept constant by pressure regulation in order to obtain reliable results from GDOES CDP. On the other hand, the effect of varying the pressure on the emission yield can be considered to be minor within the limits of practical operating conditions for most CDP applications. It is worth, however, bearing in mind that varying the discharge pressure has a significant effect on the plasma processes, and does affect the emission yield when these variations are large. The experimental results obtained for the emission yield are related to the results from theoretical model calculations published on the subject.