Thank you for the photos, Flyingdiamonds. I wish they were a bit larger so I could SEE these cool effects a little better! FWIW, fluorescence and phosphorescence are not bad at all. In fact, with only a few exceptions, they are considered desirable in diamonds.
Here's my shot at this:
When illuminated by UV light, some diamonds absorb high-energy radiation and re-emit it as visible light. This is fluorescence. Fluorescence is most commonly blue, but may appear in other colors, including white, green, yellow or orange. Several different fluorescent color zones may occur within one stone (need special equipment to see this).
Many people, including pros, prefer fluorescence in their diamonds, especially blue fluorescence in colorless and near-colorless stones. Blue fluorescence in these diamonds can make them appear a more highly desired “blue-white,” and really brighten stones in daylight, when non-fluorescing diamonds may appear darker.
However, yellow or orange fluorescence in a high-color stone may make the diamond appear less “white,” so this type of fluorescence is not necessarily a desired trait. It depends upon the body color of a particular diamond.
In colored stones, one should be aware if there is a very strong fluorescence in a color that is opposite the color of the stone. For example, the perceived color of a Fancy yellow diamond might be impacted by a very strong blue fluorescence because on the color wheel, blue is opposite yellow. So when the yellow stone with blue fluorescence is viewed in daylight, the two colors may cancel each other out, creating… "meh" in terms of color. On the other hand, yellow, orange, or even green fluorescence may actually enhance the appearance of a yellow diamond by intensifying the appearance of the yellow body color. This "color boost" can really be a benefit to faint and light yellow stones, for example. I'd even venture to say that a lower-alphabet light yellow diamond with medium or strong yellow or orange fluorescence could give quite a color punch while saving a bundle in terms of cost.
According to the GIA, between 25 and 35 percent of all gem-quality diamonds show fluorescence. Of these, a mere 0.2 percent show extreme fluorescence which gives diamonds a milky or greasy appearance. Because of their cloudy appearance, these few diamonds may be considered less desirable than stones with less fluorescence.
Diamonds that have “fluorescence” on their grading reports generally cost less than diamonds without fluorescence, regardless whether the fluorescence impacts appearance positively or negatively. This is because, as cool as it can be, explaining fluorescence to most shoppers is difficult and there doesn’t seem to be much of a benefit to the average buyer.
A rare number of diamonds that show fluorescence continue glowing after removal of the UV source. These diamonds are phosphorescent. Coveted Type IIb diamonds, which are semiconductive, often display phosphorescence. As clgwli wrote, the Type IIb Hope and Wittelsbach-Graff diamonds, both from India in the 17th century, show orange-red phosphorescence.