Yogurt, a popular fermented dairy product, is of different types and known for its nutritional and nutraceutical benefits. However, incorporating additives into yogurt has been adopted to improve its functionality and nutraceutical properties. Additives incorporated in yogurt may be natural or modified. The incorporation of diverse natural additives in yogurt formulation, such as moringa, date palm, grape seeds and argel leaf extracts, cornelian cherry paste, mulberry fruit and leaf powder, lentil flour, different types of fibers, lemongrass and spearmint essential oils, and honey, has been reported. Similarly, modified additives, such as β-glucan, pectin, inulin, sodium alginate, and gelatin, are also added to enhance the physicochemical, textural, sensory, and rheological properties of yogurt. Although additives are traditionally added for their technological impact on the yogurt, studies have shown that they influence the nutritional and nutraceutical properties of yogurt, when added. Hence, yogurts enriched with functional additives, especially natural additives, have been reported to possess an improved nutritional quality and impart several health benefits to consumers. These benefits include reducing the risk of cardiovascular disease, cancer, osteoporosis, oxidative stress, and hyperglycemia. This current review highlights the common types of yogurt, the production process, and the rheological and nutraceutical benefits of incorporating natural and modified additives into yogurt.