Development of new biocides has dominated human responses to evolution of antibiotic and pesticide resistance. Increasing and uniform biocide use, the spread of resistance genes, and the lack of new classes of compounds indicate the importance of navigating toward more sustainable coevolutionary dynamics between human culture and species that evolve resistance. To inform this challenge, we introduce the concept of coevolutionary governance and propose three priorities for its implementation: (i) new norms and mental models for lowering use, (ii) diversifying practices to reduce directional selection, and (iii) investment in collective action institutions to govern connectivity. We highlight the availability of solutions that facilitate broader sustainable development, which for antibiotic resistance include improved sanitation and hygiene, strong health systems, and decreased meat consumption.