The meat and milk products from domesticated ruminants are important foods within a balanced diet, offering a rich source of energy, protein, fats, minerals, and vitamins. The sensorial properties of meat and milk are mainly linked to their fat content and fatty acid composition, which are influenced by the feeding background or nutrient composition of diets. While several studies have investigated the nutritional effects on the fat content and fatty acid profile of ruminant meat and milk, as well as their relationship with sensorial properties, a comprehensive overview of these effects is lacking. This paper summarises current literature and discusses changes to fatty acid composition (including ω-3 concentrations), fattiness, and associated quality traits of sheep, goat, beef cattle, alpaca, and llama meat that can be achieved by using different forages or feeds in a total mixed ration. Additionally, it presents the shelf life and nutritional value of meat, milk, and cheeses from the milk of dairy cattle, buffalo, goats, and sheep as influenced by a ruminant diet. Further advancement in these areas will promote the sustainability of ruminant production and its associated feeding systems in achieving premium quality animal-derived foods.