Germany and holders Spain are favourites to reach next Sunday's final but must overcome respectively the weight of history and the world's most expensive player Cristiano Ronaldo to get there.
The Germans, whose exciting young side have won all their games so far, scoring nine goals along the way, have never beaten opponents Italy at a major tournament in seven attempts and are sweating on the fitness of playmaker Bastian Schweinsteiger ahead of Thursday's game in Warsaw.
However, 'Schweini' returned to training on Monday after two days on the sidelines and Germany are hopeful he will be able to shake off a nagging ankle problem in time to face the Italians.
Italy have their own injury headaches and coach Cesare Prandelli complained that the timing of the quarter-finals meant his opponents will have had two extra days to recover.
"It's a problem that UEFA must consider for the next European Championship," he told a news conference on Monday. "To play a semi with this small gap does not help the spectacle."
As in 2006, when Italy were eventually crowned world champions, the team came into the tournament with unwanted headlines at home due to a domestic match-fixing scandal.
But the Azzurri have drawn praise for playing an attractive attacking game and they had 35 shots on goal in Sunday's 0-0 draw with England in Kiev - the first game to go to extra time at the finals - before prevailing on penalties.
"Italy have been surprising at this tournament and they fully deserve to be in the last four," Germany midfielder Mesut Ozil told reporters. "There was a lot of negative stuff written about them before the tournament but they have showed how good a team they are."
BOYCOTT
The tournament, being held in eastern Europe for the first time, has been the most closely-fought in years. But for Poland's co-hosts Ukraine the successful staging of matches on the pitch has been marred by a diplomatic boycott due to the jailing of former prime minister Yulia Tymoshenko. A Ukrainian court on Monday adjourned Tymoshenko's tax evasion trial until mid-July, but that will do little to unfreeze talks on trade and other issues with the European Union, or persuade foreign leaders to attend the tournament final in Kiev.
Spain and Portugal meet in the first semi-final in the eastern Ukrainian city of Donetsk on Wednesday, with the focus on the clash of Ronaldo and his team mates from La Liga champions Real Madrid.
Madrid midfielder Xabi Alonso said Spain did not have a specific plan to counter the threat of the team's third top scorer of all time.
"We always play with the same idea whoever the opponent. In this case, we will analyse Cristiano's game and there may be small adjustments but we will try to play as a team because that's the best way to stop a player," he told reporters.
