We show that the Adam and Gibbs model of relaxation of liquid and polymeric glass-formers based on the configurational entropy, S-c, cannot account for several important experimental facts and phenomenology. These shortcomings include the decrease of the glass temperature when the glass-former is confined in nanometer pores, thermorheological complex nature of the viscoelastic spectrum of polymers, and also the deviation from a linear relation between log(relaxation time) and (TSc)(-1) found generally in fragile liquids. A closer reexamination of the Adam and Gibbs model indicates that the proposed transition rate of the cooperative rearranging regions does not seem to have captured all the complexities of molecular motion, i.e., their many-body dynamics. This aspect of the Adam-Gibbs model is improved by combining it with the coupling model to construct a modified model. The results of the modified model have the benefit of being consistent with all the experimental data considered.