Skin under the eyes is sensitive and thinner as compared to the rest of the face. This part of the face is particularly susceptible to poor nutrition, stress, lack of sleep and lifestyle issues.
Some causes of Dark Circles and Puffy Eyes can be listed below.

A) Poor blood circulation in the under eye area can lead to poor oxygenation which will result in dark circles under the eye.
The above is a direct cause of poor nutrition especially lack of Vitamin C and E in the diet.
B) Stress plays a big part in inducing dark circles under the eye.  High stress levels invariably lead to poor sleeping habits which can cause dark circles under the eyes.
Lack of sleep and rest due to lifestyle issues is a common reason for this problem.
Lack of fresh air and light exercise can also lead to under eye problems.
C) Hereditary factors can also cause dark circles. If there is a genetic predisposition to pigmentation, then dark circles under the eyes may be due to factors out of the control of the person.
D) Puffy Eyes are caused by excessive salt intake which may lead to water retention.
Poor dietary habits especially too much fat intake and excessive alcohol intake can directly lead to puffy eyes.
E) Poor sleeping position may also lead to puffy eye problems.

Some solutions recommended by beauticians and healthcare experts are given below.

a) Local application of certain bleaching agents and glycolic acids does seem to help in reducing the dark circles in many cases.
b) Local application of creams rich in vitamin C and E may also help in counteracting poor nutrition by stimulating blood flow under the eye, reducing the incidence of dark circles.
c) Some de pigmentation products like Kogic acid, used under the guidance of a trained professional can help in reducing the dark pigmentation, improving the condition of the skin under the eye.
d) Most people may find the cause to be a lifestyle related. Some light outdoor exercise in the fresh air, good deep sleep and a break from the hectic work environment will improve facial skin giving it a glow and reducing dark circles dramatically.
e) For people who suffer from dark under eye circles on a permanent basis and the cause is hereditary, it may be better to use, clever makeup and learn to live with the problem.
f) Some beauty treatments which consist of ozone treatments and skin lightening packs can also help to a certain degree.
g) A simple home remedy is to put hot (warm) and cold tea bags alternatively, directly on the closed eyes and directly above the dark circles for some relief.
Get rid of puffy eyes by putting cotton wool dipped in warm tea over the affected portion.
h) Try dipping cotton wool in cucumber juice and applying below the eyes. Keeping Cucumber pieces over the eyes for fifteen minutes a day also help in reduction of this problem.
i) Try to sleep straight on the back with a low pillow . This can help in reducing puffy eye problem.
j) A better long term solution is to modify the lifestyle to find permanent relief. Reducing alcohol intake, reducing fat intake and regular light outdoor exercise can help in improving skin under the eye and getting rid of puffy eyes.

I hope above helps. It is important to first find a cause of the beauty related problem, before rushing to the market to buy  creams and gels for the skin. Many a times, the cause may be found in poor nutrition, poor  exercise regimen and stress related issues. Some modification in the way we live combined with some short term solutions will normally improve quality of life and also external beauty.

Ref: http://www.janicebeauty.com/eyebeauty.htm