After months of negotiations, helped by Algerian intermediaries and the Shah's death, US diplomacy bore fruit.
On the day of President Ronald Reagan's inauguration, 20 January 1981, the hostages were set free. A day later they arrived at a US Air Force base in West Germany.
Here Air Force attache David Roader shouts with joy as he arrives on German soil.
In return the US had agreed to unfreeze Iranian assets worth $8bn and give hostage takers immunity.