Cabochons, also known as "cabs" , are gemstones that have been shaped and polished to give a smoothly curved  domed surface on the top.  The cabochon cut is very old: all gemstones cut prior to about 1000 C.E.  were either carved (for uses such as figurines, cameos or seals) or cabochon cut. Stones cut as cabochons today are classified either as calibrated or freeform.

 Calibrated cabochons are regular, symmetrically shaped stones that are precise standard sizes, measured in millimeters. The most common calibrated cabochon shapes are round, oval, square, marquise (shaped like an  eye or an oval with pointed ends) , and pear (teardrop). Freeform cabs may be almost any size and shape.

Most cabochon stones generally have a flat back unless they are described as "native cut", in which case they will often have a curved back. "Native cut" stones are frequently cut on fairly primitive equipment, and often with an eye toward maximizing total stone weight, both of which contribute to the tendency of such stones to have  material below the girdle or widest edge of the stone.

 

(Cabochon gemstone jewelry by J.D. Hallowell - left to right: oval Amethyst in gold-filled; oval Malachite in sterling; marquise Rose Quartz in gold filled; square black Mother-of-Pearl in sterling; freeform Boulder opal in sterling)