It isn't illegal (yet) to own something on the CITES lists, but it is illegal to move any items on the top 2 lists between the 187 signed up countries, no matter how old those items are.
CITES is supposed to prevent the items being moved from one country to another, thus killing off international trade in endangered species and prevent those species being hunted, exported and becoming extinct. There are nearly 40,000 items on the 3 lists.
There are places where CITES don't mean a thing and others where it does. The US customs seem to be particularly keen to seize anything that looks like it might be on the list. I believe some older Gibson guitars were impounded when being sent to Canada. You don't get them back. The UK and Europe have signed up and, I assume, will be a risk to importers of restricted items.