Dissolution of glassy polymers can be considered as a combination of solvent penetration featuring Case II transport and polymer dissolution controlled by polymer disentanglement. In the present work, an anomalous transport model is developed for solvent penetration and is coupled with a disentanglement model for polymer dissolution. Solvent penetration is controlled by the relaxation or deformation of polymer and the diffusional Deborah number is shown to be a major model parameter. In the disentanglement model, dissolution of polymer molecules requires that solvent concentration be greater than a critical gel concentration and that a polymer molecule be allowed a certain time to complete the disentanglement of diffusion movement from the gel state to liquid state. This time is assumed to be equivalent to the reputation time, which is a function of molecular weight, solvent concentration and chain rigidity. A concept of disentanglement clock is introduced as the material time clock controlling the dissolution. The new model may explain many experimental observations, such as effects of type of solvent and polymer on dissolution rate and the thickness of the gel layer. Experimental studies are performed with well- characterized samples of polystyrene and poly(methyl methacrylate) in various solvents using interferometry and critical angle illumination microscopy. The solvent concentration profiles and dissolution rates are measured using ellipsometry. The necessary self-diffusion coefficient of the polymer is measured by pulsed gradient spin echo NMR spectroscopy. In addition, experimental studies are performed using poly(acrylic acid) and poly(vinyl alcohol) in water to study the influence of ionic conditions on dissolution.