Actually, there are two different ways a that tea can be decaffeinated. the first is a chemical process using a chemical compound called ethyl acetate. the second is simply introducing the leaves to CO2 gas. The first is what most companies use (because it's cheaper), but can leave chemicals. The second is much safer, but more expensive for companies (this is what adagio uses).
There is also a third option called "home decaffeination" in which regular (caffeinated) tea leaves are infused and then infused again ... the second batch is almost completely caffeine-free (just as close as those other processes can get!). Companies cannot use this method due to the fact that the leaves have a very short drinking life after they have been infused.
Hope this helps,