There are a number of organic solutions to your problem. One includes crushing coffee beans and spreading them onto your eye-bags. Another, and more popular solution is to chill two thin slices of cucumbers and apply them onto your closed eyes for 30 minutes.
Bags may very likely be the result of lack of sleep. There are however over the counter treatments and creams that can be applied to the area to reduce the appearance of under eye bags.
It may be because of allergies,diet,dehydration,stress,too much salt and alcohol. Reduce usage of salt and alcohol.If it's due to fatty tissue deposits, remove them through surgery.
Dr. Oz just stated on his tv show last week that many people who have bags under their eyes have allergies. So he recommended taking an over the counter antihistamine such as benadryl before going to bed at night. He also recommended wet tea bags to be placed gently over the closed eye.
i heard of using a cold compress twice daily. For example, an ice pack, or even cucumber slices would help. Surgery is really the only permanent solution to getting rid of the bags.