Transport models of diffusion-induced bubble growth and collapse in viscous liquids are developed and evaluated. A rigorous model for these important phenomena is formulated taking into account convective and diffusive mass transport, surface tension, and viscous and inertial effects. Predictions for bubble growth dynamics demonstrate the importance of viscous effects in the liquid surrounding the bubble for a wide range of conditions having relevance to polymer processing operations. It is also shown how previous models employing various approximations can be derived from the rigorous model by using different mathematical methods and dimensional analysis. Predicted bubble growth dynamics from the rigorous and approximate models are compared to establish the ranges of validity for two commonly used approximations. These comparisons indicate that models using a thin boundary-layer approximation have a rather limited range of applicability. A new approximate model based on a previously published result, gives reasonably accurate bubble growth rate predictions with a significant reduction in computational effort.