Flourescence
Many diamonds emit a visible light called fluorescence when they are exposed to ultraviolet (UV) radiation. It is caused by interaction between the UV radiative energy and the diamond atoms.
Under the right conditions, you can see fluorescence in about 35 percent of gem diamonds.
Blue is the most common fluorescent colour, but other possible colours include white, yellow and orange.
For decades, jewellers believed that fluorescence had influence on diamond's colour and fluorescence had a great impact on the price. The impact was sometimes positive and sometimes negative depending on intensity and the colour of fluorescence. Recent researches show that fluorescence doesn't have any influence on face-up colour.

Most of the diamonds on this brooch emit blue fluorescence.
Phosphorescence is very rare. Only a few diamonds, type II b, emit phosphorescence. It is an interesting phenomenon but it does not have any effect on diamond’s colour.