© Denzil Green
A Pizza-Wheel Cutter is a rotating wheel blade with a handle meant for using in cutting up a pizza into slices for serving.
The wheel blades on them will be 3 to 4 inches (7 1/2 to 10 cm) wide. The larger the wheel, the more quickly it cuts.
Some makes have wheels with wavy edges on the blade, to give your slices scalloped edges. Some have dual blades (the blades are more end to end, rather than side to side.) Some have a blade guard on them. This is useful both for safety during use, and to help stop it scratching other things when stored in a drawer.
Some have a hole in their handles, letting them be hung up if desired for storage. At the blade end of handle, there is usually a finger guard to stop your fingers approaching the blade. Some modern ones have no handles, just a big blade guard on the top that you press down on.
The wheels can loosen over time and wobble. Some models have a mechanism that can be used to tighten the wheel support back up. When they start to wobble, or get dull, they can drag toppings with them. Some less well designed models might not have enough clearance between wheel and frame to stop cheese getting stuck.
Pizza-Wheel Cutters with a bit of heft to them can mean that you have to press less.
Not all are dishwasher-safe.
Not everyone needs a Pizza-Wheel Cutter, or to slice pizza, period: almost all delivered pizza comes already sliced. But you will need to slice a pizza if you make it yourself, or, usually, if you buy frozen. The cutters can, however, also be used for other food items such as fudge, taffy or lasagne, etc.
Some people say that often a good chef’s knife is better.
Literature & Lore
In July 2009, a 28-year old woman was asked for proof of age ID when purchasing a pizza cutter from the branch of Marks and Spencer in Derby, England. Marks and Spencer said the cashier was right to follow policy, only selling bladed items to people over 18, and asking anyone who looks younger than 25 to produce as proof of age ID. 
 Jamieson, Alastair. Woman, 28, told to prove age to buy pizza-cutter. London: Daily Telegraph. 27 July 2009.