There are a number of ways to reduce under-eye dark circles. You can try a Retinol cream or gel or a vitamin-A product; these are designed to reduce pigmentation and increase collagen. You can also try daily cool water or ice cubes to reduce puffiness under the eyes.
Other brightening products, such as those including vitamin C, or doctor-prescribed products with hydroquinone, reduce melanin production and skin discoloration.
You can also take a daily antihistamine if your dark circles are allergy-related. Caffeine-based products and other facial creams and gels are designed to help with allergy-related dark circles.
Another method to reduce discoloration and improve skin condition is to try laser treatments and chemical peels. These methods provide longer-lasting solutions. If you need a more intensive solution, you can ask your dermatologist about hyaluronic acid fillers.