Dark circles under the eyes are known to be signs of stress, lack of sleep, fatigue, malnutrition, allergies etc. They can have an enormous effect on your appearance. Luckily you can easily make them disappear naturally or by applying some some ingredients or products to the affected area.
The easiest and healthiest ways to remove dark circles would be by getting plenty of sleep, rest, increasing your water intake at least 8 glasses of water a day & last but not least eating well.
Sometimes applying natural products like cooled tea bags & sliced cucumbers can help reduced the puffiness
Beauty products can also do the trick. Peter Thomas Roth AHA / Kojic Acid Under Eye Brightener, Oleda Time machine for dark circles, Emergin C Lighten-Up, Under eye Circle Fighter are all products well know for diminishing dark circles under eyes.