Increased strategic thinking is needed about antimicrobial use and antimicrobial resistance (AMR), which has been termed the quintessential One Health challenge and compared to greenhouse gas emissions (GHG) mitigation or abatement. The parallels between these wicked problems are indeed striking. AMR is characterised by market and institutional failures in terms of externalised costs by antimicrobial users and the absence of global regulatory or governance architecture. Multiple human and animal sources of antimicrobial pollution exist that are further complicated by complex environmental interactions, pooling, and persistence. Multiple potential entry points could be used to modify clinical and veterinary uses of medicines and detect and diagnose AMR. Many interventions complement or interact in unanticipated ways and the human dimension to antimicrobial use raises unresolved behavioural challenges. Finally, political economy dimensions can create conflicts between public and private sector interests and the interests of developed and developing countries. These conflicts can inhibit innovation and the adoption of even the most technically effective measures. Overall, the science policy discourse can seem incoherent and overwhelming. Recourse to One Health, planetary boundary, or ecosystem service rhetoric can only go so far. An immediate question is what to do first, or how to set priorities for action, on the basis of a consensus of what is and isn’t known.