The genetic progress achieved by animal breeding programs may be affected by genotype-by-climate interactions (GxC). This systematic literature review assesses the scientific evidence for GxC on multiple traits of cattle, pigs, and poultry. Two search engines (Scopus, Web of Science) were queried for original peer-reviewed scientific (English full-text) studies. We included (1) observational studies and designed experiments considering dairy or beef cattle, swine, chicken or turkeys, where (2) at least one production, fertility, or health trait was tested for GxC, (3) the existence of GxC was tested directly based on temperature, relative humidity, or climatic indices for heat or cold stress, and (4) genetic effects within a breed or line were investigated. The search resulted in 46 eligible studies, with a (low) risk that the requirement of full-text English studies may have resulted in some work not included in this review. Our review shows an increase in GxC studies from 2015 onwards. Cattle was the most studied species (n = 36; 78.3%), whereas eligible studies on turkeys were lacking. Climatic parameters used in the studies ranged from well-known parameters (e.g., temperature, temperature-humidity index) to more complex indices combining temperature, relative humidity, wind speed and solar radiation. All observational studies (n = 40; 87.0%) used weather station data. In total, 75 traits were studied, which were predominantly production traits regardless of species. Studies on fertility and health traits have been emerging from 2010 onwards, but their numbers still lag far behind those for production traits. Genotype-by-climate interaction was confirmed in 54.0% of the study outcomes. This systematic review shows that little is known about the role of GxC in health and fertility traits in cattle, and for all traits in pigs and poultry in general. As current evidence shows that genotype-by-climate interaction is common across species and traits, we suggest to collect detailed climatic data and use them to assess the presence of GxC in indoor and outdoor production systems, as well.