[Discussion] Dark undereye circles and puffiness - causes, treatment, management.

This was inspired by the popularity of my quick comment on the topic in the 30+ thread. Undereye circles have a variety of causes and will have different symptoms and treatments. It's possible to have a combination of several problems. I apologize for the lack of scientific references, I'm simply too lazy and making this post took longer than expected. Without further comment, this is the extent of my knowledge. Please comment to add any information or your experiences!

#Brown circles

Caused by hyperpigmentation from sun exposure, rubbing or hormonal problems. Sometimes genetic, more common if you have darker skin, but can happen with lighter skin too.
Prevent by using sunscreen, having good UV screening sunglasses, not rubbing the eyes.
Treat with ingredients that fight excessive pigmentation like vitamin C, mild retinoids, licorice root extract, arbutin, linoleic acid, niacinamide... This thread on lightening ingredients by effect may be useful.
Hide with yellow based correctors.

#Purple circles

Caused by circulation and drainage problems and congestion (sometimes caused by allergies or infections), capillary fragility.
Prevent by sleeping on your back to minimize the effect of gravity on blood pooling. Dehydration can cause capillary fragility so stay hydrated.
Treat with ingredients that promote circulation like caffeine, green tea and vitamin K. Horse chestnut extract and flavonoids (especially oligomeric proanthocyanidins) help strengthen capillary walls. Some medical conditions like undergoing dialysis or diabetes can cause lowered vitamin C levels in the body which has been linked to capillary fragility, supplementation may be effective in these cases. There isn't much research on skin oils but some of them are claimed to have capillary strengthening effects (rosehip seed oil, hazelnut oil, neroli oil, rose oil) and circulation improving effects (coriander oil, eucalyptus oil, cypress oil, evening primrose oil, geranium essential oil). There is anecdotal evidence in this thread that if you have persistent sinus problems a nasal spray (specifically Flonase) can be quite effective.
Hide with orangey correctors. Yellow correctors are the opposite on the color wheel but using the opposite color can create an ashy effect on skin.

#Grey/blue circles

Caused by genetics (eye position in the socket and the amount of adipose tissue under the skin); thin skin (skin can be naturally thin, thin with age, prolonged use of some steroids can cause skin thinning); fatigue, stress and lack of sleep.
Prevent by using antioxidant ingredients, stopping smoking and using sunscreen. UV damage and smoking can cause premature skin aging, including thinning skin. Get enough rest.
Treat with ingredients that help thicken the skin by boosting collagen production like retinoids, vitamin C and zinc. Keeping the skin moisturized helps plump it up, too. If it's stress and fatigue related nourising and cooling eye masks may help.
Hide with salmon and peach correctors.

#Puffiness and bags

Caused by circulation problems, allergies, congestion (can be a co-symptom of purple circles), fluid retention (fatigue, hormonal), or genetically having quite thick fat pads under the eyes (can start sagging with age).
Prevent by sleeping on your back to make it more difficult for blood to pool under the eyes; staying hydrated and not using too much salt. As skin loses elasticity with aging and becomes more "loose" it could allow more fluids and blood to pool in the undereye area, so helping elastin production with anti-aging ingredients could be preventative.
Treat with caffeine, green tea and vitamin K, cool compresses. Massages can help with fluid retention. You could make green tea ice cubes, wrap them in gauze so they aren't too cold, and use them as a compress, pressing gently from the corner of the eye outward to massage. Caffeine is great because it also helps if the cause is having naturally above average fat deposits under the eyes - it helps shift the cell metabolism from accumulating to burning fat, so the fat cells in the hypodermis shrink. Anti-inflammatory ingredients can help with swelling if it's caused by allergies or chronic infections. If you have allergy or chronic congestion problems do consult with your doctor.
Hide with a concealer slightly lighter than your skin, applied only in the shadow of the eye bag. Applying a lighter concealer on the bag itself will highlight it. Some facial primers and skincare products designed for undereye bags have a film former than can help tighten and compress the area. The facial primers tend to be ones designed for aging skin and have to sort of smoothed on, not patted on, for the film former to work the best.

Quick edit to add - dark circle colour can be affected by skin pigmentation.

Blue and purple circles can show up as more brownish or grayish with darker skin.

Blue circles can sometimes appear somewhat purplish too, especially on very pale skin. Since it is blood vessels showing through the skin with very deep set eyes and/or thin low pigmentation skin the amount of vessels showing though can be nearing the look of lack of circulation or capillaries leaking blood.

Extreme purple circles can look almost dark blue.