Anagama kiln
The Anagama kiln is an ancient type of pottery kiln brought to Japan from China via Korea in the 5th century.
An anagama (a Japanese term meaning "cave kiln" ) consists of a firing chamber with a firebox at one end and a flue at the other (note that although the term "firebox" is used to describe the space for the fire, there is no physical structure separating the stoking space from the pottery space).  The term Anagama describes single-chamber kilns built in a sloping tunnel shape.  In fact, ancient kilns were sometimes built by digging tunnels into banks of clay.
The anagama is fueled with firewood, in contrast to the electric or gas-fueled kilns commonly used by most contemporary potters.  A continuous supply of fuel is needed for firing, as wood thrown into the hot kiln is consumed very rapidly.  Stoking occurs round-the-clock until an appropriate temperature is reached.  Stoneware and porcelain pieces will typically mature at "cone 10", a gauge of "heat work" dependent on the final temperature coupled with the time required to achieve that temperature (see pyrometric cone).  Somewhat inaccurately, cone 10 could be thought of as a temperature range as high as 2375 F (1300 C).
Burning wood not only produces heat  up to 2,500 F (1400 C)  it also produces fly ash and volatile salts.  Wood ash settles on the pieces during the firing, and the complex interaction between flame, ash, and the minerals comprising the clay body forms a natural ash glaze.  This glaze may show great variation in color, texture, and thickness, ranging from smooth and glossy to rough and sharp.  The placement of pieces within the kiln distinctly affects the pottery's appearance, as pieces closer to the firebox may receive heavy coats of ash, or even be immersed in embers, while others deeper in the kiln may only be softly touched by ash effects.  Other factors that depend on the location include temperature and oxidation/reduction.  Besides location in the kiln, (as with other fuel fired updraft kilns) the way pieces are placed near each other affects the flame path and thus, the appearance of pieces within localized zones of the kiln can vary as well.  It is said that loading an anagama kiln is the most difficult part of the firing.  The potter must imagine the flame path as it rushes through the kiln, and use this sense to paint the pieces with fire.
The length of the firing depends on the volume of the kiln, and may take anywhere from 48 hours to 12 days or more.  The kiln generally takes the same amount of time to cool down.  Records of historic firings in large Asian kilns shared by several village potters describe several weeks of steady stoking per firing.

# Kiln variants
One variant on the anagama style is the waritake kiln.  A waritake kiln is akin to anagama in structure, but it has partition walls built every several meters through the length of the kiln.  Each partition can be side stoked.
A Noborigama  chambered climbing kiln is also built on a slope, and each succeeding chamber is situated higher than the one before it.  The chambers in a noborigama are pierced at intervals with stoking ports. Climbing kilns have been used in Japan since the 17th century.  The Renboshiki noborigama is a multi-chambered climbing kiln.  There are many distinguishing characteristics between the noborigama and anagama style.  For example, an anagama is somewhat like a half-tube (long vault) with a fire burned at the lower end.  A noborigama is like a set of half-tubes (arches or short vaults, buttressing each other) placed side-by-side with piercings that allow each chamber to feed into the next.
The jagama (snake kiln or dragon kiln) is related to anagama, noborigama, and waritake kilns, and was used extensively in China for thousands of years.  Jagama are tube shaped similarly to anagama kilns, but they can be very long -- 200' (60 m) is not unreasonable.  Although partitioned and side stoked, jagama do not have partition walls, rather, improvised walls are created by densely stacking pottery at intervals.

# Characteristics of climbing kilns
The main advantage of climbing kilns is that heat from the burning fuel is re-used, the same heat heating more than one part of the kiln.  Exhaust  heat created during firing of the lower part of the kiln, preheats the chambers above.  In addition, the cooling ware and walls below preheat the incoming air.  Thus, firing of ware in the upper chambers requires only the additional fuel needed to bring the ware, walls and air to peak temperature. (From a thermodynamic point of view, the higher temperature of combustion and cooler exhaust suggest greater efficiency.)  The fuel efficiency of this type of design may have been essential for high temperature ceramics to be economically viable in Asia long (perhaps a thousand years) before the use of coal in Europe.  (A modern type, called a tube kiln improves the efficiency and output still further by having the ware move through the kiln in a direction opposite to that of the hot gasses.)
All of these kilns use two counter-flow exchange mechanisms to maintain the air supply and to change the ware being fired, with minimal loss of heat.  Each of these exchanges works on the same principle as countercurrent exchange, the principal difference being that the ware is not a fluid.
An advantage of the chambered and semi-chambered variants appears to be that they are partly downdraft, which makes the firing results less sensitive to the way the ware is loaded.
A disadvantage of (small) climbing kilns is a tendency to rapid cooling, caused by the incoming air.