Get Rid of 'Em!
I will separate these into two sections, one to hide them and one to get rid of them. They are usually caused by one of three things: genetics, respiratory allergies, and thin skin. If your mom has under eye-shadows as well, chances are, you have this because of genetics. Symptoms of wheezing, sneezing, and watery-itchy eyes can cause the tissues underneath your eyes to get swollen and inflamed. Also, if the skin under your eyes is very thin, blood vessels and darker pigmentation are more obvious.

To Get Rid of Them
Keep alcohol-free toner or freshener in the fridge. Pour some on cotton balls and put it on closed eyes for a couple of minutes.
Put chamomile tea bags on your eyelids to lessen puffiness, because regular tea can stain your skin.
While vitamin K has been used for years to minimize bruises and broken blood vessels, K-enriched creams have recently been clinically proven to fade those ugly under eye circles that are par for the course after late-night study sessions.
Eye gels can be used to take away puffiness, dark circles, and fine lines. They are lightweight, soothing and revitalizing to tired eyes. Always apply eye gels with your ring, or fourth, finger – it’s the weakest of all your fingers, and won't tug as much on the delicate eye area.
Try to get about 8 hours a night and drink as much water as you can stand. This will make your skin look clearer and prevent puffiness.
The old chilled cucumber compress really works. It’s a “procedure” because you’ll need 15 uninterrupted minutes and a few slices of cold cucumber. Lie down with your head and feet elevated, and apply the disks to your closed eyes. Relax for 15 minutes. There are also some great eye balms that reduce puffiness and darks circles (it’s good to keep them in the fridge, too).
Peel a cucumber and slice it up. Throw it into a blender or food processor and totally puree it. Add a little water if needed for blending. Place this mixture, covered, in the fridge until cool. When needed, place a couple tablespoons of the mixture on a damp paper towel. Fold into the shape of an eye patch and place on eyes for 15 minutes. Lie down on the couch or on your bed to relax while doing this. The remaining mixture can be saved in the fridge for one week. The cucumber has a remarkably soothing scent, and will actually de-puff your eyes. Putting it on your face won't hurt either.
Everyone knows cucumber on the eyes soothe and feel good. But, if you slice up raw zucchini and soak it in ginseng or chamomile tea and place the slices on your eyes, you'll get a “de-puffing” treatment as well as a soothing one. Cool the tea before applying the zucchini soaked slices. Cut a few extra, put them in a container covered with the tea and store them in the fridge. When you need to relax, pull a few out, let them warm up a little to cooler than room temp, and sit back and relax. Don't leave them in the fridge long enough to spoil and don't put them on your eyes if they look like a science experiment.
Also, as part of your daily routine to prevent puffs in the first place, apply under eye cream using a bit of pressure with your finger in a "rolling" motion from inner to outer corners. This will help with lymphatic drainage.
Cut down (way down) on salt and hold back on the water or other liquids one hour before bedtime.
Apply a moistened tea bag on the eyes for 10 minutes. Use black teas because the tannic acid is stronger in this type of tea. Use an eye gel or cream that contains coneflower. This has been used to diminish lines with some good success. Use a concealer with a yellow-green base to minimize redness in the eyes. If you use eyeliner, apply a thin line. Heavy lines will draw attention to tired puffy eyes.
Chill a potato in the fridge. Cut two slices from the spud and spritz the eye area with water. Lie down, and place the potato slices over your eyelids. Leave them in place for ten minutes and then remove. Wipe the eye area with a cool cloth.
Wet cotton rounds in ice water and place over your eyes for five minutes. For added de-puffing power, first apply a chilled eye gel.
Getting a restful night's sleep can also help in preventing puffiness and dark circles. Lavender promotes sleep-inducing alpha waves and if you sprinkle a few drops of Lavender oil on a hanky and put it inside your pillow, you will get some good sleep.
To reduce puffiness around the eyes, pour leftover chamomile tea into an ice tray and freeze. After a late night when skin looks fatigued, wrap a couple of these chamomile ice cubes in a face cloth and press gently around closed eyes for a few minutes.
1) The best overall eye tonic is eyebright (an herb). Make a tea of it and either use the teabags or soak cotton balls or soft gauze in the tea and apply to eyes as a compress while lying down.
2) For puffy and swollen eyes, make a wet compress of 4 tablespoons freshly grated raw potato. Place on the eyes for about 15 minutes, and then rinse with cold water.
3) To reduce swelling and for bags under the eyes, brew a cup of strong rosehip tea. Soak 2 cotton balls in the tea or use 2 tea bags, lie down and place over the eyes.
4) For dark circles, cut a fresh fig in half, place a half over each eye.
5) To soothe tired, irritated eyes, cut the end of a cucumber into ¼-inch thick slices. Apply a cool slice to each eye. Raw potato slices laid on sore eyes reduces heat and redness.
6) For eye puffiness, any tea bag (herbal is better, especially eyebright), slightly cooled, placed on the eyes while you rest.
7) For tired or bloodshot eyes, soak sterile cotton balls or soft cloth in cold skim milk. Place over eyes for 10 minutes. Rinse entire face in warm, then cool, water.
8) To lighten dark circles under your eyes, wrap a grated raw potato in cheesecloth and apply to eyelids for 15-20 minutes. Rinse with warm water.