112

is the single emergency number in Iceland, representing all the response parties to accidents, fire, crime, search, rescue and natural disasters on land, at sea, or in the air. Additionally, Iceland‘s child protection officers can be reached through 112.
The emergency dispatchers are on duty around-the-clock, all year around. When you dial 112 they respond at once and immediately send the appropriate assistance.
The role of Emergency Alert 112 is to provide a friendly, efficient and reliable service.
112 can be reached anywhere in Iceland, from any telephone, by voice or by SMS

They also have a app.
The 112 Iceland app can be used for two things, both for added safety on your Iceland trip.
First of all you can call for help by pressing the red Emergency button. Your location will be sent by text message to the 112 response center. Remember that even though your phone shows no signal there is a possibilite that you can send text message.
The green Check In button is for you to leave your location with us so if something happens we have more information to worked with. Only the 5 last location’s are stored and we recommend you use this – don’t worry – you are not disturbing anyone – except for our big computer who wants to be disturbed.
Here you can download the app for Android phones, Windows phones and iPhone.