CUT refers to the proportions, symmetry and finish of a polished diamond. To get from the raw diamond to the cut gemstone requires the skilled hand of a master cutter. The better the CUT proportions, the better the diamond handles light to create sparkle. Therefore CUT is the single most important factor affecting a diamond's sparkle, brilliance and visual fire as illustrated with the following diagrams for a round brilliant-cut stone:
A well-cut diamond reflects maximum light and so sparkles the best.
Well-cut
Shallow-cut and deep-cut diamonds let the light escape at the sides or bottom
Shallow 
Deep
The sad fact is, 75% of all rounds and 88% of all other shapes on the market are poorly proportioned to retain carat weight rather to maximise sparkle.
A well-cut diamond loses more of the rough diamond than deep or shallow cuts as illustrated below.
Natural rough diamond
2 diamonds cut with well-cut proportions. For example this may yield a larger diamond of 1 carat and a smaller diamond of 0.5 carat
2 diamonds cut to retain maximum carat weight and not ideal sparkle proportions. For example, this may yield two diamonds of around one carat.
There are three components to diamond brilliance: white light return, dispersion and scintillation. White light return is the percentage of light observed coming out of a diamond. Dispersion, sometimes called fire, is the break-up of white light into the rainbow of spectral colours. Scintillation is the sparkling aspect of a diamond when it is moved. All of these factors are finely related and need to be balanced carefully by the cutter as maximising any one will decrease the other aspects.
The CUT proportions of a diamond affects its price, sometimes by as much as 40%! HRD, GIA, AGS and IGI certificates give grades for cut quality for round brilliant diamonds. The most research has been done so far on what proportions contribute to the sparkle of the round shape - due the the 360 degree symmetry of the round shape, it is easier to define a set of parameters for proportions.
The term fancy shape diamond is used to describe all other diamond shapes that are not round brilliant e.g. princess, pear, emerald cut, radiant, cushion, asscher, oval, heart, marquise...etc.
Unlike round brilliant diamonds, there are no defined range of proportions which can be used to predict in advance whether a fancy shape diamond (e.g. princess, pear, emerald cut, radiant, cushion, asscher, oval, heart, marquise...etc) is well-cut.
The AGS has the only system capable of grading fancy shapes as their grading takes into account light performance rather than diamond proportions. Whilst AGS grading is possible for a number of fancy shapes, so far there are very very few AGS ideal graded fancy cut diamonds available on the market - as princess cuts are the most popular fancy shape, in practice the very few AGS ideal cut reports tend to be for princess cut diamonds.
The HRD, GIA and IGI grading reports are more prevalent for all shapes but do not give any cut proportion grades for fancy shape diamonds (as diamond proportions analysis cannot be as readily applied to fancy shapes as it can be for round brilliant diamonds). Hence, with the exception of AGS Ideals, the best way to judge a fancy shape diamond and whether its well-cut is to see it!
CUT is confusingly also used to refer to diamond SHAPE.
There are a number of shapes which diamonds traditionally take, depending on the original nature of the rough, uncut stone.
The most popular shape for a diamond is the round brilliant diamond which is aptly named as when well-cut, the round diamond reflects the maximum light and sparkles more than any other shape. They are also slightly more expensive than any other shape because 50% of the rough diamond is lost when cutting a round shape and less is lost when cutting any other shape.
After the round brilliant diamond, princess cut diamonds (a square shape) are the most popular. For example, out of 100 diamonds produced: 80-85% will be round brilliants, 5-10% will be princess cut diamonds and the remainder will be spread across all the other shapes possible e.g. pear, emerald cut, cushion, asscher, radiant, heart, oval, marquise, trilliant...etc
Round Brilliant Oval Pear
Emerald Marquise Heart Radiant
Princess Asscher (Square Emerald) Cushion Trillion
