Glazes are the glass skins that cover clay bodies to make them food safe, colorful, or resistant to water.  They can be made of many combinations of flux (temperature regulating materials), alumina (minerals and chemicals that affect color and surface appearance), and glassformers (bulk material that forms the base for the other materials to melt into). 

Although there is an infinite variety of glaze available, they mainly fall into classes of glazes such as these:

Shino glaze is a generic term for a family of pottery glazes. They tend to range in color from milky white to a light orange, sometimes with charcoal grey spotting, known as "carbon trap" which is the trapping of carbon in the glaze during the firing process

Celadon glazes come in a variety of colors, including white, grey, blue and yellow, depending on the thickness of the applied glaze and the type of clay to which it is applied. The most famous celadon range in color from a very pale green crackle to deep intense green, like shades of jade. The color is produced by iron oxide in the glaze recipe or clay body. Celadon are usually fired in a reducing atmosphere kiln.

Tenmoku (also spelled "temmoku" and "temoku") is a dark glaze with a surface that resembles oil spotting.  Crystallized iron clusters provide spots of a silvery shimmer.

Red iron oxide saturate glaze is a highly variable glaze the runs from rich clear brown to a mottled deep red or orange rust color. 

Cobalt glaze is standard in pottery lines for its reliablility and pure deep blue color.

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Ash glaze is made by accumulations of pure ash as it develops in a wood firing.  The ash from the wood used to fuel the kiln lands on the pots, collects, and melts to form a glaze at around cone 10-14, depending on the wood used.  Ash glaze can be fluxed down to lower temperatures by adding ash to existing lower temperature glazes or by using ash as an ingredient and mixing it with other lower melting materials.

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Salt glaze is a gaseous residue glaze formed when salt is vaporized during firing and lands on the work forming a light grey or grey blue glaze, traditionally over cobalt decoration.

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This is not a comprehensive array.  There are many other classes of glaze like copper reds, kaki, plum, chun red, and crackle, just to name a few.  Glazes with specific names like "Toshiko green" are named after specific people that made and shared their recipe.  "Toshiko green" is a satin matte soft green glaze named after a woman named Toshiko Takaezu.

Glazes also vary in ways that are not apparent, like the temperature that they mature and the chemicals used to create the effects.  The technical specs on glazes have traditionally remained the secrets of pottery families and dynastic lines.  In the modern clay era, glazes are shared and modified among potters all over the world.  The glazes a particular potter uses are chosen due to very personal and individual desires in the mind and eye of the potter.  Some potters blend the glazes they use from raw materials and chemical recipes or furmulas, others buy manufactured glazes and add materials to them, and others buy and use bottles of glaze.  The manner of application and layering and combinations of different types of clay and glaze allow for infinite varieties of glaze effects and every pottery tends to develop a specific style that they are known for over time.

One glaze applied to 5 different clay bodies will have five different looks, varying in accordance with the chemical properties of the clay.  When pots are at the point of vitrification, when they turn to rocks, they are molten, like lava, and there is a free exchange of the material in the clay and the material in the glaze.  If you look very closely at a pottery shard that was fired to vitrification, you will see three distinct layers, the clay, the joined layer, and the glaze.  Some potters use this to their advantage by painting the surface of the clay with slips that are different from the clay body, creating more than one finish on one pot.

Another factor in the way a glaze looks is how it is fired, the free access to oxygen as it is heated or the restriction of oxygen, reduction.  Reducing the available oxygen to the ware as it fires forces the atmosphere to pull materials in the clay to the surface of the ware, creating a simmering glass shell on the pots when at full melt that allows other materials in the clay to boil to the suface and become trapped.  Reduced ware tends to have more depth in the color and texture of the pure glaze and is greatly admired for this.  Oxidation environments allow for free access to oxygen, allowing the glaze to pull what it needs from the atmosphere instead of the body of the pot.  This leaves the glaze "cleaner" more pure in color and with less texture. 

Traditionally, reduced looking work could only be produced in combustible fuel kilns, but modern technology and chemistry has allowed for standard oxidation firing electric kilns to produce similar results by varying the formulas of the clay or glaze.  The world of firing is changing and the changes are very exciting.  People are firing electric kilns to high fuel kiln temperatures and lowering the firing temperatures of wood kilns to create a more efficient firing.  The world of firing is opening in the face of thousands of years of traditional results.  Some people are embracing it while others look towards the traditional practices and materials to preserve the heritage and legacy of generations of potters who have passed the knowledge they discovered through family and corporate lines.

Pure glaze decoration is part science, part art, part craftsmanship, and part heritage.  Every one who has ever had a favorite cup has been a part of its history.