Resistance to therapeutic antimicrobial agents is recognized as a growing problem for both human and veterinary medicine, and the need to address the issue in both of these linked domains is a current priority in public policy. Efforts to limit antimicrobial resistance (AMR) on farms have so far focused on control of the supply and use of antimicrobial drugs, plus husbandry measures to reduce infectious disease. In the United Kingdom and some other countries, substantial progress has been made recently against targets on agricultural antimicrobial drug use. However, evidence suggests that resistant pathogenic and commensal bacteria can persist and spread within and between premises despite declining or zero antimicrobial drug use. Reasons for this are likely complex and varied but may include: bacterial adaptations to ameliorate fitness costs associated with maintenance and replication of resistance genes and associated proteins, horizontal transmission of genetic resistance determinants between bacteria, physical transfer of bacteria via movement (of animals, workers, and equipment), ineffective cleaning and disinfection, and co‐selection of resistance to certain drugs by use of other antimicrobials, heavy metals, or biocides. Areas of particular concern for public health include extended‐spectrum cephalosporinases and fluoroquinolone resistance among Enterobacteriaceae, livestock‐associated methicillin‐resistant Staphylococcus aureus, and the emergence of transmissible colistin resistance. Aspects of biosecurity have repeatedly been identified as risk factors for the presence of AMR on farm premises, but there are large gaps in our understanding of the most important risk factors and the most effective interventions. The present review aims to summarize the present state of knowledge in this area, from a European perspective.