If you are the registered owner of the car/vehicle, you can visit My pages on Ísland.is under Assets - Vehicles - My vehicles, where you can download the vehicle´s history. If you are thinking about buying a car/vehicle then you can request the seller to provide the vehicle´s history stating this. It indicates whether there is a mortage on the vehicle, but it only states yes/no, but no further information. The District Commissioners can provide a mortage cerficate that is more comprehensive, for a fee. The mortgage certificate can be accessed here: https://island.is/en/mortgagecertificate