The ‘organic’ label guarantees a production process that avoids the use of synthetic fertilisers, pesticides and hormones and minimises the use of veterinary drugs; however, consumers are demanding guarantees regarding food quality. This article reviews the current state of knowledge on the quality of organic animal products, including the authentication of their organic origin. Quality has been considered as an integrative combination of six core attributes: commercial value, and nutritional, sensory, technological, convenience and safety attributes. The comparison of these attributes between organic and conventional animal products shows high heterogeneity due to variability in farming pratices in both organic and conventional systems. To overcome this, we pinpoint the farming practices underlying the differences observed. This enables light to be shed on the consequences of possible trajectories of organic farming, if specifications are relaxed or tightened up on commitments concerning farming practices that impact product quality. Two recent meta-analyses showed better nutritional attributes in organic milk and meat linked to their higher poly-unsaturated fatty acid (PUFA) content, particularly n-3 PUFAs. Regarding safety, we point to a lack of integrated studies quantifying the balance between positive and negative effects. Organic farming reduces the risk of drug residues and antibiotic resistance, but both outdoor rearing and a frequently longer rearing period increase the animals’ exposition to environmental contaminants and the risk of their bioaccumulation in milk, eggs, meat and fish flesh. We highlight antagonisms between quality attributes for certain animal products (lamb, pork). In general, attributes are more variable for organic products, which can be explained by lower genetic selection (poultry), lower inputs and/or greater variability in farming conditions. However, the literature does not address the implications of this greater variability for the consumers’ acceptability and the necessary adaptation of manufacturing processes. Further research is needed to document the impacts on human nutritional biomarkers and health. Methods used to authenticate organic origin are based on differences in animal diet composition between organic and conventional systems, but their reliability is hampered by the variability in farming practices.