Crystals can be mined (at the moment) by any one mining asteroid fields. They will not appear from Drone mining and are a random spawn. You can also get crystals through certain in game events. At one time crystals could be used to enhance devices during crafting. But after a terrible accident this practice was halted. You can read about that over here.
Now Crystals are collected from you and Traded in for Research Academy Points. These can then be spent in the Research Academy‘s to launch projects to improve items.
Crystals are Red, Blue, Green, Yellow and Grey.