The past two decades have witnessed a global surge in the application of probiotics as functional ingredients in food, animal feed, and pharmaceutical products. Among food industries, the dairy industry is the largest sector where probiotics are employed in a number of dairy products including sour/fermented milk, yogurt, cheese, butter/cream, ice cream, and infant formula. These probiotics are either used as starter culture alone or in combination with traditional starters, or incorporated into dairy products following fermentation, where their presence imparts many functional characteristics to the product (for instance, improved aroma, taste, and textural characteristics), in addition to conferring many health-promoting properties. However, there are still many challenges related to the stability and functionality of probiotics in dairy products. This review highlights the advances, opportunities, and challenges of application of probiotics in dairy industries. Benefits imparted by probiotics to dairy products including their role in physicochemical characteristics and nutritional properties (clinical and functional perspective) are also discussed. We transcend the traditional concept of the application of probiotics in dairy products and discuss paraprobiotics and postbiotics as a newly emerged concept in the field of probiotics in a particular relation to the dairy industry. Some potential applications of paraprobiotics and postbiotics in dairy products as functional ingredients for the development of functional dairy products with health-promoting properties are briefly elucidated.