Fire cupping
Fire cupping is a method of applying acupressure by creating a vacuum next to the patient's skin. In traditional Chinese medicine (TCM) it involves placing glass, plastic, or bamboo cups on the skin with a vacuum.  The therapy is used to relieve what is called "stagnation" in TCM terms, and is used in the treatment of respiratory diseases such as the common cold, pneumonia, and bronchitis.  Cupping is also used to treat back, neck, shoulder, and other musculoskeletal pain.  Its advocates claim it has other applications as well.  This technique, in varying forms, has also been found in the folk medicine of Vietnam, the Balkans, modern Greece, Mexico, and Russia, among other places, including Iran where it is called 'bod-kesh' meaning literally 'pull with air'.

# Method
Instead of using a vacuum pump, a vacuum is created by air (heated by fire) in a glass cup placed flush against the patient's skin.  As the air cools in the cup, a vacuum forms that pulls up on the skin, stimulating the acupressure effect.
The cups are usually roughly bell shaped with a capacity of about 4 fluid ounces.  Most commonly, a total of from 8 to 12 cups are applied to the subject's back in two parallel 'vertical' columns, midway between the spine and each edge of the body, spaced about 4 inches on center within each column.  An interesting animation of the process may be found here  (requires Shockwave Flash).
There are several ways of heating the air in the cup with fire:
1. One can swab rubbing alcohol (minimum 90%) into the bottom of a cup, then light it and place the cup immediately against the skin.  By creating the seal the immediate loss of oxygen puts the fire out, preventing the person from being burned.  The smaller the amount of alcohol, and the quicker the flame is extinguished by application of the cup, the better, so long as there is no risk of the cups falling off due to lack of a proper seal.
2. One can hold the cup inverted over a flame (e.g. a lit candle), heating the air, then place the cup immediately against the skin.  Care must be taken not to heat the glass itself.  Even so, the person to whom the cup is applied will feel distinctly more heat than in the previous method.
3. One can ignite a flame with a small alcohol-soaked cotton wad resting on a small pad of leather or other insulating material that rests directly on the patient's skin, then place the cup immediately over the flame, putting out the fire.  The quickness with which the flame is extinguished depends on the size and shape of the cup.
Methods 1 and 2 heat the glass to some extent and have a risk of burning the patient if not carefully executed.  Method 3 risks the cotton falling off the insulating pad onto the patient's skin, and leaves the pad and cotton wadding inside the adhering cup which could be considered cumbersome.
Baby oil massaged onto the skin first causes a better seal to form, making it possible to use this therapy with less heating of the cup.  It is often possible to slide the adhered cup around on the skin, preserving the suction seal as it glides.  Care must be taken not to move the cup over protruding moles, skin tags, scabs, etc.
The longer a cup is left on, the more of a circular mark is created.  The skin pores are more open, and the patient may have a feeling like sunburn.  An application of about 20 minutes is average, for the back; however this varies with the individual.  In no case should the cups be left in place if the subject reports noticeable discomfort.
According to the American Cancer Society, "vailable scientific evidence does not support cupping as a cure for cancer or any other disease". It can leave temporary unsightly marks on the skin and there is also a small risk of burns. Persons who claim this therapy to be beneficial report that its effect is a long lasting feeling of relaxation and invigoration.  It is possible that whatever relief is obtained by this procedure is derived from the same principles that are employed in shiatsu massage, where instead of the outward sucking of the cups, strong inward pressure is directed at the muscles of the dorsal ribcage and abdomen.
Cupping was commonly used as a Eastern European Jewish folk remedy, with the Yiddish name  (bankes).
The proverb '       (Es vet helfn vi a toyten bankes, literally "It would help like cupping a corpse") is used to opine that a course of action would be futile.

# Wet cupping
In this variant, a form of bloodletting also called blood cupping, a small scratch or incision is made with a lancet prior to the cupping, and the pressure difference extracts blood from the skin.
Islamic traditional medicine uses this technique - called in Arabic hijamah or hijama - with a number of hadith supporting its recommendation and use by Muhammad (although Muhammad is said to have explicitly stated, roughly put, to have as much knowledge in things that need skill as any average person).