Important addition I'd like to add here is that you almost certainly won't owe any US tax. You just need to file the return. AFAIK You get a crazy high deduction and can also deduct all your local taxes, so it's almost always 0 or near 0 taxes owed. That said it can be expensive to actually prepare and file the return, as you need to find a tax specialist proficient in Local AND US tax law to prepare it for you and they charge higher than normal rates.

Another thing to know is that the US imposes worldwide reporting requirements on banking institutions for their US citizen customers. This problem is far less severe than it initially was, but depending where you go some banks/institutions may deny or restrict your access to financial products because they don't want to deal with the reporting requirements attached to you. Again, it's probably fine anywhere in Europe (nowadays anyway), but elsewhere in the world it may be extremely difficult to do something as simple as get a simple checking account.