Yogurt is a major fermented milk product providing probiotics, lactic acid bacteria, vitamins, calcium, and proteins, yet health-beneficial phenolics, flavonoids, anthocyanins, and iron are absent in plain yogurt. These compounds could provide antidiabetic, antiobesity, antimicrobial, and anticancer properties. Here, we review the effect of adding natural functional ingredients in dairy and non-dairy yogurts, with focus on the properties and biological activity of functional yogurts. Properties include color, pH, acidity, water-holding capacity, syneresis, viscosity, structure, fats, microbiology, and flavor. Biological activities comprise antioxidant, antidiabetic, antiobesity, anti-inflammatory, cardioprotective, antibacterial, and anticancer. We found that yogurt from plant-based milk, such as common bean and soy milk, and the addition of functional ingredients, enhanced biological activities of yogurts and improved properties. Functional ingredients provide polysaccharides, phenolics, flavonoids, anthocyanins, and amino acids. Functional ingredients are both natural stabilizers and texturizing materials. The incorporation of functional ingredients improved the contents of phenolics and flavonoids by 96.52 and 97.72%, respectively, increased water-holding capacity by 20–25%, and improved the number of viable cells of lactic acid bacteria. Incorporation reduced syneresis by 15–32% and decreased the loss of fat globules. Moreover, apparent viscosity, texture, microstructure, and sensory properties were enhanced. Biological activities strongly increased, especially antioxidants, which increased from 4.88 to 15.03 mg trolox equivalent per 100 g of yogurt.