Antimicrobial resistance (AMR) is a major global public health threat, typically represented by bacteria becoming resistant to antibiotics, and hence harder to treat. A particular concern is multidrug resistance, which can arise as bacteria acquire new AMR genes via horizontal gene transfer (HGT). In the important nosocomial pathogen Staphylococcus aureus, bacteriophage (phage, viruses of bacteria) are the major drivers of HGT of AMR by the process of transduction. In an initial systematic review, I found that dynamics of transduction and the overall contribution of this process to the global spread of AMR are unclear. In this thesis, I aimed to fill this research gap through an interdisciplinary approach, combining mathematical modelling, lab work, and analysis of routinely collected hospital data. I first investigated the dynamics of phage and S. aureus, including generalised transduction of AMR, by developing a novel mathematical model representing these dynamics, and generating in vitro data to parameterise this model. I estimated rates of generalised transduction, and showed that this process consistently leads to generation of multidrug-resistant bacteria, even in the absence of a selection pressure. Within-host however, phage may often be present alongside antibiotics. These may either act in synergy to kill bacteria, or antibiotics may limit phage predation and instead exert a selective pressure on multidrug-resistant bacteria generated by phage via generalised transduction. I extended my model to include antibiotic pharmacodynamics, and parameterised this by generating additional in vitro data. By analysing this extended model, I identified timings and concentrations of phage and antibiotics which maximise bacteria killing, whilst minimising the risk of multidrug resistance evolution and selection. Finally, I translated these findings to an in vivo setting by analysing 20 years of routinely collected pseudonymised hospital data on more than 20,000 patients colonised or infected by S. aureus. Using antibiograms of more than 70,000 isolates, I identified evidence of within-host AMR phenotypic diversity, and changes in that diversity over time, potentially mediated by transduction. Overall, the work presented in this thesis clarifies some of the complex phage-bacteria dynamics in S. aureus, and highlights the important role played by phage in AMR spread through generalised transduction.