There are no universally accepted grading systems for any gemstone other than white (colorless) diamond. Diamonds are graded using a system developed by the Gemological Institute of America (GIA) in the early 1950s. Historically all gemstones were graded using the naked eye. The GIA system included a major innovation, the introduction of 10x magnification as the standard for grading clarity. Other gemstones are still graded using the naked eye (assuming 20/20 vision).
For the past several hundred years, gemstones have been broken down into two categories; precious and semi-precious. Though today we think primarily of diamond, ruby, sapphire, and emerald as "precious", these categories are based mainly on fashion and the composition of these two lists has changed frequently over time.
Recently a mnemonic device, the "four C's" (color, cut, clarity and carat), was introduced to help the consumer understand the factors used to grade a diamond. With modification these categories can be useful in understanding the grading of all gemstones. The four criteria carry different weight depending upon whether they are applied to colored gemstones or to colorless diamond. In diamonds, cut is the primary determinant of value followed by clarity and color. Diamonds are meant to sparkle, to break down light into its constituent rainbow colors (dispersion) chop it up into bright little pieces (scintillation) and deliver it to the eye (brilliance). This is a function of cut. In its rough crystalline form, a diamond will do none of these things, it requires proper fashioning and this is called "cut". In gemstones that have color, including colored diamonds, it is the purity and beauty of that color that is the primary determinant of quality.
Physical characteristics that make a colored stone valuable are color, clarity to a lesser extent (emeralds will always have a number of inclusions), cut, unusual optical phenomena within the stone such as color zoning, and asteria (star effects). The Greeks for example greatly valued asteria in gemstones, which were regarded as a powerful love charm, and Helen of Troy was known to have worn star-corundum.
A factor in determining the value of a gemstone is called water. Water is an archaic term that refers to the combination of color and transparency in gemstones; used hierarchically: first water (gem of the finest water), second water, third water, byewater.
Historically gemstones were classified into precious stones and semi-precious stones. Because such a definition can change over time and vary with culture, it has always been a difficult matter to determine what constitutes precious stones.
Aside from the diamond, the ruby, sapphire, emerald, pearl (strictly speaking not a gemstone) and opal have also been considered to be precious. Up to the discoveries of bulk amethyst in Brazil in the 19th century, amethyst was considered a precious stone as well, going back to ancient Greece. Even in the last century certain stones such as aquamarine, peridot and cat's eye have been popular and hence been regarded as precious.
Nowadays such a distinction is no longer made by the trade. Many gemstones are used in even the most expensive jewelry, depending on the brand name of the designer, fashion trends, market supply, treatments etc. Nevertheless, diamonds, rubies, sapphires and emeralds still have a reputation that exceeds those of other gemstones.
Rare or unusual gemstones, generally meant to include those gemstones which occur so infrequently in gem quality that they are scarcely known except to connoisseurs, include andalusite, axinite, cassiterite, clinohumite and bixbite.
Gems prices can fluctuate heavily (such as those of tanzanite over the years) or can be quite stable (such as those of diamonds). In general per carat prices of larger stones are higher than those of smaller stones, but popularity of certain sizes of stone can affect prices. Typically prices can range from 1USD/carat for a normal amethyst to 20,000-50,000USD for a collector's three carat pigeon-blood almost "perfect" ruby.