Alkaloid found in coffee, tea, cola, guarana paste, yerba mate and kola nuts.
Caffeine and its constituents are thought to convey antioxidant benefits when consumed orally. Studies have looked at oral consumption of caffeine-containing beverages followed by exposure to UVB light (the kind that causes sunburn and skin tumors) and found that compared with those who drank decaffeinated beverages, the drinks with caffeine conveyed a protective benefit.

Applied to skin, caffeine may have anti-inflammatory properties. It has a constricting effect on skin, which can help reduce redness but may also be irritating. It doesn’t work on everyone for facial redness, and in fact some may find it worsens the problem.

Caffeine’s popularity in products related to cellulite is due to its distant relationship to aminophylline (a pharmaceutical once thought to reduce cellulite), which is a modified form of theophylline.

There is no substantiated research proving theophylline can affect cellulite, but researchers have disproved aminophyilline’s claimed impact on cellulite.

There are only two studies showing caffeine to have benefit for reducing cellulite. One was conducted by Johnson & Johnson, which owns the RoC and Neutrogena brands, both of which sell (or once sold) cellulite creams that contain caffeine. The other was conducted by cosmetics ingredients manufacturers that sell anti-cellulite compounds.
There is no independent research showing that caffeine can provide any benefit for treating cellulite.

When it comes to puffy eyes, there is no research indicating caffeine can have this benefit when applied topically. However, caffeine does have potential as an antioxidant, so it isn’t totally useless in skin-care products.

It is used as a stimulant and flavoring in lipsticks, to aid ingredients to penetrate the skin, and to stimulate the skin.

Sources
Food Chemistry and Toxicology, September 2012, ePublication
Milady’s skincare ingredients dictionary
Paula’s Choice Beautypedia
BMC Complementary and Alternative Medicine, March 2006, http://www.biomedcentral.com/1472-6882/6/9
Bioscience, Biotechnology, and Biochemistry, November, 2005, pages 2219–2223
Obesity Research, July 2005, pages 1195–1204
Sports Medicine, November 2001, pages 785–807
Journal of Cosmetic Science, July–August 2002, pages 209–218
Journal of Investigative Dermatology, July 2009, pages 1,611–1,613
Photochemistry and Photobiology, March-April 2008, pages 330-338
Carcinogenesis, August 2005, pages 1,465–1,472
caffeine contains theophylline: Progress in Neurobiology, December 2002, pages 377–392