My elastic, wire, silk and thread are nutotious for getting tangled and unravelling of their own accord. The best way I have found for storing them is on a mug tree that keeps the thread separate and easily accessible. 

 
Occasionally either I loose or break the little plastic cuffs that stop the thread unravelling. Luckily I have some elastic replacements that I bought from Beadalon. 

Handy!