Icelandair now offers you the option to check-in with your mobile phone.
With mobile check-in you can check-in 22 hours before departure and pick a seat on-board the aircraft. 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 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 travelling without baggage you can go straight to the gate.