The BBC's Richard Galpin, in Athens, said the celebrations were wild, with tens of thousands of people going "completely berserk and mad".
He said that in the early hours of the morning, police joined the celebrations by using their van's loudspeakers to broadcast the excited commentary from the "silver goal" across the city.
There is a sense of revamped national pride which will allow them to look forward to the Olympics rather than the great concern and anxiety of recent months, he said.
Making the final is an incredible achievement for Greece. It must have been quite a scene in Athens.
What happened to the players' strike threat? There is no news of that today, nor was there any sign of a problem on the pitch. They executed a brilliant if dour defensive plan, and kept the ball when given the opportunity. They ran like mad and somehow outlasted the Czechs, as they finally began to trouble their opponents' goal in extra time. Rob Hughes has a negative, but informed account of the Greek's "Teutonic" tactics. Update: In How have Greece done It?, Mike Adamson and Rob Smyth describe the reasons behind Greece's remarkable success, without letting their personal distaste for defensive tactics color the piece. Recommended.
What to make of this spirited performance, coming on the heels of a strike threat? One would have thought that conflict within the camp would disrupt preparations and wear away team unity. But playing for your team - and they've played as a cohesive unit throughout the tournament - and country is sufficient motivation I suppose, even when you are at odds with bureaucrats at the Football Association.
Sunday it's Portugal vs. Greece. Given the Greek's style, close marking will choke the match of flair and skill, but they - including their raucous fans - should make it interesting nonetheless. Can they win the whole thing against a skilled Portugese side that has finally come good? The market at Betfair rates them at odds of about 5-2, so it's not inconceivable. But two things are certain. Greece will make life difficult for Portugal, and they have proved the doubters wrong repeatedly thus far.