Shortly and simply: no restrictions. :)
Quotes from wiki, who quoted blue posts:
They don’t have a level requirement so we do intend to see them used
as a way to twink new characters, or allow people to buy into gemming
up a bit earlier on if they have the gold.
There may be some interesting complications with this though.
You can pay an artisan to remove the gems from an item. The last
design I had heard of was that it was based on gem value, so as you
socket higher level gems it becomes more expensive, but you’ll almost
certainly want to unsocket gems to level them up, or swap to new gear.
This may cause some unique problems for low level (non-twink)
characters attempting to buy high level gems and then being unable to
remove them from the socket when they get a better piece of armor
(because they can’t afford it), but that may turn out to be an
acceptable roadblock.
Source: http://www.diablowiki.net/Gem