Significant challenges to worldwide sustainable food production continue to arise from environmental change and consistent population growth. In order to meet increasing demand, fish production industries are encouraged to maintain high growth densities and to rely on antibiotic intervention throughout all stages of development. The inappropriate administering of antibiotics over time introduces selective pressure, allowing the survival of resistant bacterial strains through adaptive pathways involving transferable nucleotide sequences (i.e., plasmids). This is one of the essential mechanisms of antibiotic resistance development in food production systems. This review article focuses on the main international regulations and governing the administering of antibiotics in finfish husbandry and summarizes recent data regarding the distribution of bacterial resistance in the finfish aquaculture food production chain. The second part of this review examines promising alternative approaches to finfish production, sustainable farming techniques, and vaccination that circumvents excessive antibiotic use, including new animal welfare measures. Then, we reflect on recent adaptations to increasingly interdisciplinary perspectives in the field and their greater alignment with the One Health initiative.