Crazing is the result of the body and glaze expanding at different rates during the firing process and looks like tiny cracks that cover the entire piece. Very often people make the mistake of assuming it occurs over time and is the result of age. Actually, one could take a piece of pottery today and force it to craze. A lot of older American dinnerware crazed for various reasons. Some potteries had not mastered the proper rates between the body and glaze. Others had problems controlling the temperatures with the periodic bottle type kilns. Dinnerware often crazed, but it wasn't necessarily noticeable.
As a crazed piece is used, it starts to get discolored. The crazing on some dishes may be invisible, but continued use creates discoloration and it gets worse over time. This can be especially true for covered butter dishes and covered casseroles. The lids may look perfectly normal, but the bases can look greasy and dirty. No amount of soap and water can clean up such pieces.
There is at least one way to clean up a crazed piece of dinnerware: soaking in peroxide. The small bottles of peroxide sold in pharmacies won't work. It has to be the stronger peroxide sold in beauty shop supply stores. The procedure is simple, pour the peroxide into a container such as a small plastic tote, place crazed piece inside so that it is completely submerged, and cover the container.
Below are before and after pictures of a piece I recently cleaned up. It is a Taylor, Smith & Taylor hotel ware bowl from circa 1910. It is essentially white ware that was given a clear glaze. I purchased it on eBay knowing the condition. There are no chips or cracks, but it has severe discoloration because of the crazing. The after pictures were taken one week after soaking in a peroxide bath. There are a few spots here and there and another round should clear it up completely. The all-over crazing is still there, but the dirt and residue been cleaned.
There are a few things to remember if you attempt to use a peroxide bath. Use clear peroxide -- not the creamy kind. NEVER use bleach such as Clorox. It will whiten very quickly, but it will compromise the clay and the piece could crumble. Also, gold and platinum trim can be affected by peroxide. I've tried some pieces in the past, but notice care must be given when cleaning the ware afterwards.
You may want to try the procedure on an inexpensive piece before attempting to clean up something valuable and/or rare.