Diamonds come in a variety of colors, some of them highly prized (pinks, blues, even yellow). However in a white diamond, the presence of a yellow tint will lower the price of a diamond. The less body color in a white diamond, the more true color it will reflect, and thus the greater its value.
Alexandrite is renowned for its strange optical properties – it can actually undergo dramatic shifts in color depending on what kind of light it's in. To be clear: this color change is independent of your viewing angle; a gemstone that shifts colors when you rotate it in your hand is said to bepleochroic, and while alexandrite is strongly pleochroic, it can also change colors independently of viewing angle when viewed under an artificial light source. (In natural sunlight, the gem appears greenish blue; in soft incandescent light, the gem appears reddish purple, instead.)
A variety of Chrysoberyl, alexandrite belongs to the same family of gemstones as emerald. It's color-changing properties (and its scarcity relative to diamond) is due to an exceedingly rare combination of minerals that includes titanium, iron and chromium.