Origins of Sharpening Stones:
The Japanese have traditionally used sharpening stones which are lubricated with water to sharpen their metal tools. As they have been doing this for many hundreds of years, it is obvious that the first stones were those which were found occuring naturally. The geology of Japan provided a type of stone which consists of fine silicate particles in a clay matrix.
This is somewhat softer than Novaculite which is the mineral which forms what is commonly called an "Arkansas" or "Washita" stone. Novaculite is from the Devonian period and Mississippian periods (roughly about the time that cockroaches first appeared on earth 410-325 million years ago) It is a sedimentary rock composed mostly of microcrystalline quartz and is basically a recrystallized variety of chert. It is also the primary material in "Charnley Forest" and "Turkey" oilstones.
Japanese stones are also sedimentary but I've been unable to find out much about their geological history. Some say that they are composed of volcanic materials but I can't confirm that. The most famous are typically mined in the Narutaki District just North of Kyoto.
Advantages of Japanese Water Stones:
These softer Japanese stones have a few advantages over harder stones. First, because they are softer they do not get glazed or loaded with the material they are sharpening. New particles are constantly exposed as you work with the and thus they continue to cut consistantly. Second, they can be lubricated effectively with water (rather than oil) so nothing but a bucket of water is required. Finally, because they are soft, the worn material and the water form a slurry which in conjunction with the stone, sharpens and polishes the blade. The disadvantage should be obvious... they wear out faster.
Grades of Japanese Water Stones:
Historically there are three broad grades of sharpening stones. The Ara-to, or "rough stone", The Naka-to or "middle/medium stone" and the shiage-to or "finishing stone". There is a fourth type of stone which is used, but not directly. That is the nagura which is used to form a cutting slurry on the shiage-to or finishing stone which is often too hard to create the necessary slurry. Converting these names to absolute grit size is difficult as the classes are broad and natural stones have no inherent "grit number". But if I were pressed, the Ara-to is probably 500-1000 grit. The Naka-to is probably 3000-5000 grit and the Shiage-to is likely 7000-10000 grit.
The Rise of the Artificial or Ceramic Sharpening Stone:
Although there is a certain amount of romance associated with using stone which is found naturally, there are some problems with this. First, over hundreds of years, the best mines have given up much of their best stones. This scarcity causes high prices for a good quality consistant stone. Lesser quality stones have problems of consistancy and may have occasional larger pieces of grit or soft spots. With this in mind, and with modern technologies, artifical stones came to the market. There have been a variety of formulations over the years and the quality of artificial stones continues to increase.
For most users artificial stones offer many improvements over the natural stones of the past. In fact, I prefer them to the natural stone (of unknown provenance) that I have. In my opinion, the best of the artificial stones so far are the Shapton stones. Because of the way they are made they are less porous than the typical artificial waterstone and do not require the soaking that other artificial or natural stones require. They cut quickly and and seem to wear longer than the other stones on the market. It is clear that the era of the natural stone is over for all but the most traditional craftsman or specialists. The high cost and difficulty of obtaining quality natural stones make them impractical for most.
Note that I am ignoring the whole art of sharpening and polishing swords. As an art by itself, there are a greater number of steps and more specialized processes.
An explanation of the basic polishing process is here: Process
You can find materials and stones here: Namikawa Heibei
And for some words from a master sword polisher: Kenji Mishina
Link to Shapton's website: Shapton USA