The gut is a major reservoir of human pathogens, and increasing antimicrobial resistance (AMR) in these organisms is an important problem. Selection of AMR by antimicrobials occurs against a background of disruption in a rich bacterial ecosystem, the gut microbiome. Our understanding of this has recently been transformed by new techniques, such as metagenomic sequencing, that can describe the whole community and directly detect AMR genes. Efforts to control AMR would be greatly helped by reliable measures of the impacts of different antimicrobials on the gut microbiome, but these are generally not available. The aim of this thesis is to address this problem. A significant limitation of using metagenomic sequencing to study AMR is its inability to detect important resistance genes present at low abundance, and in initial work I explore methods to improve the detection of these using plasmid DNA extraction and selective culture-enrichment. These approaches improve the limit of detection of specific resistance mechanisms, but prove unsuitable for use in a quantitative assay. I then analyse data from an observational study that I conducted, which recorded antimicrobial exposures and collected stool samples from hospital patients and healthy volunteers. Using multiple regression models with data from metagenomic sequencing, I estimate the effects of specific antimicrobial exposures on global microbiome diversity, the abundance of specific taxa, and the abundance of specific classes of AMR genes. The study utilised both cross-sectional and longitudinal sampling frames, which I analyse separately, providing independent estimates that are supportive of one another. These data allow the direct, quantitative, comparison of many different antimicrobials used in the study. The work also develops approaches to the analysis of these types of observational data that could be used in future studies.