This article reviews the development of molecular healing models that couple squeeze flow and intermolecular diffusion. Historically there are a few studies that combine these processes for fusion bonding of thermoplastic composites. The motivation of this work was to develop similar models for welding of polymer films and films to substrates. These models are theoretically developed and experimentally verified. It was found that the time dependence for squeeze flow is of the same order of magnitude as that for intermolecular diffusion, making models for these processes indistinguishable experimentally, and therefore, they were assumed to occur simultaneously. Furthermore, it was found that healing of the weld can be better defined as a function of time and temperature instead of temperature alone, as historically done for welding applications. Comparison of the weld strength predictions with experimental data for impulse welds showed that the developed models were able to predict weld strength over a wide range of parameters. In Part 2, moving heat source heat transfer models together with the coupled squeeze flow and intermolecular diffusion model are used to predict healing during laser micro-welding.