Low aqueous solubility of active pharmaceutical ingredients (APIs) presents one of the greatest and most frequent challenges to formulation scientists. An estimated 75% of pharmaceutical compounds under development suffer from poor solubility. The formulation of drug/polymer amorphous solid dispersions (ASDs) is one of the most successful strategies for improving the oral bioavailability of poorly soluble APIs. Hot-melt extrusion (HME) is one method for preparing ASDs that is growing in importance in the pharmaceutical industry. HME involves the combination of an API and a polymer, which are heated and intensively mixed to yield a homogeneous product. Despite the growth in the application of HME to drug development, there are still substantial gaps in our understanding regarding the dynamics of drug dissolution and dispersion in viscous polymers as well as physical stability (phase separation and API recrystallization). Computational models have been built in order to predict optimal processing conditions (e.g. temperature, residence time, drug loading), but they are limited by the lack of supporting data for key mass transport parameters. A key omission is the lack of experimental data on the API diffusion coefficient at conditions relevant to HME. This dissertation reports the first measurements of API diffusion in pharmaceutical polymer melts at temperatures relevant to the HME process, by means of high-temperature PFG NMR. These measurements were performed in the absence of any solvents, for a range of drug loadings, temperatures, polymer systems and drug species. The mechanism of the diffusion process and its relationship to viscosity was explored with the Stokes-Einstein and Arrhenius models. Viscosity plots obtained from the rheology experiments uncovered the possibility of HME processing at significantly lower temperatures to reduce the risk of thermal degradation. Additional characterisation of extrudates prepared 30◦C below the drug’s melting point concluded that satisfactory ASDs were produced. Furthermore, this dissertation includes 1H solid-state NMR relaxometry measurements as an insight into physical state, phase separation and API/polymer interactions in extruded formulations. HME products were found to have formed successful ASDs, with no evidence of crystalline drug remains or of phase separation. This was not the case for a physical mixture that had been heated up, but not actively mixed; meaning that extrusion is indeed required (and not just high temperatures) to achieve ASDs. Chemical shift changes suggested intermolecular associations between the drug and the polymer. These interactions were studied in greater detail through a range of novel solid-state and molten-state 2D NMR experiments. The results not only corroborated the existence of drug-polymer H-bonding, but also the presence of Van der Waals interactions between the two species. Finally, several theoretical models were applied to predict solubility and dissolution rate of a drug in a polymer melt. This involved the calculation of the interaction parameter and the construction of a miscibility-solubility phase diagram. A simple static spherical particle dissolution model was fitted with the diffusion coefficient parameters measured in previous sections and the results were in agreement with experimentally obtained time-to-dissolution observations. This positive result highlighted the value of measuring the diffusion coefficient of drugs in polymer mixtures for predicting system behaviour and optimising process parameters.