Trapping is a thing here in Germany, but not on the kind of property I lease for hunting as it belongs to the forest service and they don't allow it.
Mostly due to altercations with non-hunters.
You can only trap fox, badger, weasels, pine Martin, stone Martins and raccoons (yes we have introduced raccoons). Raccoon dogs and golden jackals do not live in this area, and it is illegal to trap wolves.
I have thought about putting traps in my yard for Martens. But they can't be killing traps, they have to be live traps and you are limited on what kind of bait you can use. Most guys catch a lot of rats and stray cats.