The Order of the Falcon. The Order of the Falcon was established in 1921. It is the only Icelandic order. It may be conferred upon Icelanders and non-nationals for achievements in the interest of Iceland or in the international arena. The President of Iceland is the Grand Master of the Order. A council of five members controls the affairs of the Order and makes recommendations on awards to the Grand Master. On festive occasions, however, the Grand Master may award the Order without recommendations of the Order Council.

The Grand Master and the Chairman of the Order Council sign the Letter Patent.  The Order has the following classes: Grand Cross, Commander with a Star, Commander, and Knight.  Receipts for the insignia of the Order are to be sent to the Secretary of the President of Iceland who is the Secretary of the Order and occupies a seat on the Order Council.

On the death of a person upon whom the Order has been conferred, the insignia shall be returned forthwith to the Secretary of the Order. Abroad, the insignia may be handed to Icelandic Embassies or Consulates for further dispatch.

A Grand Cross Knight shall upon receiving the award return the Commander's Star if it has previously been awarded to him or her, as also a Commander shall return a Knight's Cross if he or she had it before.

Medals. The medal of Icelandic Red Cross was established in 1949. It is awarded by the President of Iceland for humanitarian deeds and has two classes.  Since 1954, the President of Iceland has awarded medallions for services rendered.  The President of Iceland also awards medallions of the Republic of Iceland for heroic achievement. Established in 1950, they are awarded in two classes to those who endanger their lives or health to save Icelanders from mortal danger.

Foreign medals. By presidential decree in 1947, Icelandic nationals who are awarded foreign medals must obtain the permission of the President of Iceland before they are accepted and worn.