Poorly controlled background genetics in animal models contributes to the lack of reproducibility that is increasingly recognized in biomedical research. The laboratory zebrafish, Danio rerio, has been an important model organism for decades in many research areas, yet inbred strains and traditionally managed outbred stocks are not available for this species. Sometimes incorrectly referred to as 'inbred strains' or 'strains', zebrafish wild-type lines possess background genetics that are often not well characterized, and breeding practices for these lines have not been consistent over time or among institutions. In this Perspective, we trace key milestones in the history of one of the most widely used genetic backgrounds, the AB line, to illustrate the dynamic complexity within an example background that is largely invisible when reading the scientific literature. Failure to adequately control for genetic background compromises the validity of experimental outcomes. We therefore propose that authors provide as much specific detail about the origin and genetic makeup of zebrafish lines as is reasonable and possible, and that the terms used to describe background genetics be applied in a way that is consistent with other fish and mammalian model organisms. We strongly encourage the adoption of genetic monitoring for the characterization of existing zebrafish lines, to help detect genetic contamination in breeding colonies and to verify the level of genetic heterogeneity in breeding colonies over time. Careful attention to background genetics will improve transparency and reproducibility, therefore improving the utility of the zebrafish as a model organism.