Icelandair now offers you the option to check-in with your mobile phone at m.icelandair.com
With mobile check-in you can check-in 22 hours before departure and choose your seat assignment in advance. You can then print out your boarding pass at a self-service kiosk at the airport, saving time by bypassing the check-in line.
If you are travelling with baggage you have to check –in your baggage at the self-service centre at the airport and get a bag tag for each piece. When you have checked-in at the self service centre for your flight it will be handled (fast bag drop- off) by an employee of the airline in question. If you are traveling without baggage you can go straight to the gate.