At our library, they give you the card and an ID. You can then register online to see what has been checked out. My kids don't even know about the online site, and I'm the one that set up everything. I can just type in their ID and password, and find out what has been checked out.
The county has the same sort of system here. I was just at the library and wanted to find out how much she owed in fines and pay the amount down if it was getting close to having her privileges suspended. My GD spent about half her time with us since her mom was single and worked as an RN on the night shift. Consequently her shifting back and forth between two houses meant some things were always in disarray. Library book returns and fines were one of those things.