Milk and colostrum have high biological potential, and due to their natural origin and non-toxicity, they have many uses in cosmetics and dermatology. Research is ongoing on their potential application in other fields of medicine, but there are still few results; most of the published ones are included in this review. These natural products are especially rich in proteins, such as casein, β-lactoglobulin, α-lactalbumin, lactoferrin, immunoglobulins, lactoperoxidase, lysozyme, and growth factors, and possess various antibacterial, antifungal, antiviral, anticancer, antioxidant, immunomodulatory properties, etc. This review describes the physico-chemical properties of milk and colostrum proteins and the natural functions they perform in the body and compares their composition between animal species (cows, goats, and sheep). The milk- and colostrum-based products can be used in dietary supplementation and for performing immunomodulatory functions; they can enhance the effects of certain drugs and can have a lethal effect on pathogenic microorganisms. Milk products are widely used in the treatment of dermatological diseases for promoting the healing of chronic wounds, hastening tissue regeneration, and the treatment of acne vulgaris or plaque psoriasis. They are also increasingly regarded as active ingredients that can improve the condition of the skin by reducing the number of acne lesions and blackheads, regulating sebum secretion, ameliorating inflammatory changes as well as bestowing a range of moisturizing, protective, toning, smoothing, anti-irritation, whitening, soothing, and antiaging effects.