Infectious diseases come at a huge societal and economical cost. This has recently been shown by the COVID-19 pandemic. Looking forward, arguably the largest threat is antimicrobial resistance (AMR). As pathogens develop resistance against currently available antimicrobials (e.g., antibiotics) and as the development of new antimicrobials has stalled, we are risking an estimated 10M deaths per year globally and a US$100 trillion costs to the world economy by 2050. We here propose a Centre for Doctoral Training on Engineering Solutions for Antimicrobial Resistance, with the overall aim of training physical scientists and engineers with the specialist research skills as well as broad contextual skills to create rapid impact targeting the AMR challenge. This includes different disciplines and wider aspects such as commercialisation/translation, public-health context, regulation and standardisation, implementation and adoption, public awareness and perception, and communication. Identifying key research areas that depend on cutting-edge research advances in engineering and physical sciences, our Centre for Doctoral Training focuses on preventing the spread of infection, on surveillance and diagnostics, and on antimicrobial and vaccine development. By designing and delivering our training programme with public health institutions, multinational businesses, SMEs and charities, we maximise the impact of such research on addressing the public health threat of AMR and on exploiting business opportunities that are also associated with solutions to it.