Following the classical concepts developed by Simon [Z. Anorg. Allg. Chem. 203, 219 (1931)], vitrification in the cooling of glass-forming melts is commonly interpreted as the transformation of a thermodynamically (meta)stable equilibrium system into a frozen-in, thermodynamically nonequilibrium system, the glass. Hereby it is assumed that the transformation takes place at some well-defined sharp temperature, the glass transition temperature Tg. However, a more detailed experimental and theoretical analysis shows that the transition to a glass proceeds in a broader temperature range, where the characteristic times of change of temperature, tauT=-(TT), and relaxation times, tau, of the system to the respective equilibrium states are of similar order of magnitude. In this transition interval, the interplay of relaxation and change of external control parameters determines the value of the structural order parameters. In addition, irreversible processes take place in the transition interval, resulting both in an entropy freezing-in as well as in an irreversible increase of entropy and, as a result, in significant changes of all other thermodynamic parameters of the vitrifying systems. The effect of entropy production on glass transition and on the properties of glasses is analyzed here for the first time. In this analysis, the structural order-parameter concept as developed by de Donder and van Rysselberghe [Thermodynamic Theory of Affinity (Stanford University Press, Stanford, 1936)] and Prigogine and Defay [Chemical Thermodynamics (Longmans, London, 1954)] is employed. In the framework of this approach we obtain general expressions for the thermodynamic properties of vitrifying systems such as heat capacity, enthalpy, entropy, and Gibbs' free energy, and for the entropy production. As one of the general conclusions we show that entropy production has a single maximum upon cooling and two maxima upon heating in the glass transition interval. The theoretical concepts developed allow us to explain in addition to the thermodynamic parameters also specific features of the kinetic parameters of glass-forming melts such as the viscosity. Experimental results are presented which confirm the theoretical conclusions. Further experiments are suggested, allowing one to test several additional predictions of the theory.