Milk is a highly nutritious food that contains an array of macro and micro components, scientifically proven to be beneficial to human health. While the composition of milk is influenced by a variety of factors, such as genetics, health, lactation stage etc., the animal’s diet remains a key mechanism by which its nutrition and processing characteristics can be altered. Pasture feeding has been demonstrated to have a positive impact on the nutrient profile of milk, increasing the content of some beneficial nutrients such as Omega-3 polyunsaturated fatty acids, vaccenic acid, and conjugated linoleic acid (CLA), while reducing the levels of Omega-6 fatty acids and palmitic acid. These resultant alterations to the nutritional profile of “Grass-Fed” milk resonate with consumers that desire healthy, “natural”, and sustainable dairy products. This review provides a comprehensive comparison of the impact that pasture and non-pasture feeding systems have on bovine milk composition from a nutritional and functional (processability) perspective, highlighting factors that will be of interest to dairy farmers, processors, and consumers.