Years ago, the only kind of knife sharpening there was was on a bench stone. They do still exist, but there are many more kinds of sharpeners available now for just about any kind of knife or tool. The kind of knife sharpener you choose will be determined by the kinds of things you need to sharpen.
A grinding wheel is a solid piece of abrasive stone that cuts away some of the material to reveal a sharper edge. Many different kinds of abrasive materials can be used in a grinding wheel. Aluminum oxide is the most common material and comes in different grades of oxide, differentiated by a coding system of a letter and a number. This is the best material for sharpening such hard materials as annealed iron, wrought iron, steel or bronze.
A combination that yields a very durable wheel is zirconium oxide and aluminum, known as zircon alumina. This is the second most common material for grinding, after aluminum oxide, and is a very good material for steels and alloys.
A new development in materials for grinding is ceramic aluminum oxide. This is an extremely strong material that is ideal when a great deal of precision is required. Ceramic aluminum may be blended with another material to a desired abrasiveness, depending on the item that has to be sharpened. Grinding wheels come in many shapes, with the straight wheel being the most common. A straight wheel has a cutting edge that faces front. A cylinder wheel is a drum shaped wheel, with a wide surface to cut on, on the front of the cylinder.
Grit size is very important when you have to choose the right wheel for a sharpening job. The higher the number, the finer the grit, so that a grit of 10 or 20 will be very course, and a grit of 100 or 200 will be much finer. A fine grit grinder is used for finishing work.
The old standby of a bench grinder is still the most dependable and inexpensive way to sharpen knives as well as cutters, hand tools or drill bits. A bench grinder can be mounted on a workbench to make it easier to use. The wheels can vary in size from 6 to 10 inch diameters, and usually have a motor that is 1/3 to one horsepower. The best kinds will have a place to rest the tool so it remains steady.
Chain Saw Sharpeners
These are specialized sharpeners that are used specifically for chain saws. If you use your chain saw a lot, you may want to own one. There are automatic ones the lock the chain in place when the wheel is lowered, then each tooth is set into the sharpener at an angle; the head is pulled up each time and moved to the next tooth. This will assure uniformity. Manual sharpeners are much less expensive and with proper use can be very precise. The manual lever locks the chain in place while each tooth is filed. Since many manual chain saw sharpeners come with more than one wheel, they can be used with different chains.
The essayist Ray Walberg is specifically interested in subjects relating to honing. You might discover his publications on knife sharpening at http://www.insidewoodworking.com and different sources for knife sharpening information.