In their most natural form, diamonds are - well - quite ugly. They have no luster or shine, & in fact, look like nothing more than broken glass. A diamond must be cut, and then polished before it actually becomes a thing of beauty.
Diamonds are cut with saws, into round shapes. From the rounded shape, other shapes may be cut, such as heart shapes - but the shape is less important than the quality of the cutting that is being done. If the diamond is poorly cut, it will lose light, and it will not sparkle and shine very well. Each facet of the diamond must be carefully cut into the geometrical shapes that enable the diamond to sparkle and shine, then the entire diamond is cut into a specific shape, such as an emerald cut or a princess cut diamond.
Once the cut is done, the diamond is put into a dop, which resembles a cup with another diamond - only a diamond is strong enough to smooth the edges of another diamond. Once the diamond has been cut and shaped, and had the edges smoothed in the dop, it is polished on a scaif or a diamond polishing wheel.