Dairy products from grazing ruminant have numerous positive effects on human health thanks to their higher content essential fatty acids, vitamins, and polyphenols. Compared to livestock fed a conventional maize silage- and/or grain-based diet, grass-fed livestock produce milk with higher levels of n-3 fatty acids, vitamins A, E, carotenoids, and phenols. The effect is even more pronounced if animals are grazing on legume/forbs-rich grasslands. This review argues, based on the available literature, about the effect of grazing ruminant on milk and cheese quality, including the hedonistic aspects, pointing out the link between territory and dairy products quality (Protected Designation Origin; Protected Geografic Origin; namely PDO and PGI labels). Moreover, it points out the main plant biomarkers which can be used to discriminate grazing sourced from stall-fed sourced milk and dairy products. Overall milk and cheese sourced from grazing animals (cows, sheep and goat) showed higher levels (compared to stall system) of FA, vitamins, phenols, putatively beneficial for consumers’ health. FA and plant secondary metabolites can also affect flavor and some nutritional and technological features of dairy products such as their antioxidant protection degree. This would favour a fair pricing of dairy products sourced from grazing systems and the persistence of viable and sustainable extensive production systems.