By Paul Reynolds
World affairs correspondent, BBC News website
The trip will probably dwell on historic ties rather than differences
With the US presidential election now moving into high gear, the visit by President George W Bush to the major capitals of western Europe this week, expected to be his valedictory trip, has become something of a sideshow.
The eyes of many peoples and governments in Europe will be on Senators Obama and McCain, as Europe hopes for better things from the next US president.
A poll by the UK's Daily Telegraph website in late May showed that in Britain, France, Germany and Russia, more people regarded the United States as a force for evil than for good. Only in Italy did the US fare better.
And Senator Barack Obama was the clear preference (52%) across the five countries to be the next US president.
This indicates that the mood in Europe is one for change, though it remains true that countries of the former Soviet bloc have much more positive views of the Bush administration than those in Western Europe.
This trip is largely about the Western capitals, though Mr Bush will start off at the annual EU/US summit, being held this year in Slovenia.
Iraq was a stake driven into the heart of both transatlantic ties and relations between European governments
He will then visit Berlin, Rome (including the Holy See to meet the Pope again), Paris and London, with a stop in Belfast on his way home.
Presidents in their lame-duck phase tend to travel around to say goodbye and polite hosts tend not to dwell on differences but on historic ties.
There will much of that in this visit, with a look-back at the warm feelings engendered by the Berlin airlift in 1948 and the Marshall Plan that put Western Europe back on its feet after the war.
Looking back is easy. The problems come with looking forward.
Many western Europeans would like Guantanamo Bay closed
Iraq was a stake driven into the heart of both transatlantic ties and relations between European governments. It remains, if no longer a stake, then a thorn.
President Bush's own standing has been further damaged by the memoirs of his former press secretary Scott McClellan, who said that the Bush administration had misled the world over Iraq with a "political propaganda campaign".
Iraq is regarded in many, but not all, European capitals as a historic mistake, though there is a willingness now to accept that something might be salvaged from it. As Iraq has improved, so has the transatlantic mood.
European leaders would like to hear that the US prison in Guantanamo Bay, Cuba, is to be closed and that the US will not engage in anything that could be called torture, but this will have to wait for the next president.
There will be some important issues to be discussed, though, as always on a presidential visit. These include a US push for more sanctions against Iran over the nuclear issue and a call by Mr Bush for Europe to match US spending on world health problems.
Old certainties gone
Another disappointment is that a state of Palestine, which Mr Bush became the first American president to support, has not yet come about.
Easing Russian defiance will be a key challenge for the next US leader
Mr Bush said in January: "I am confident that with proper help, the state of Palestine will emerge", and further: "I believe it's possible - not only possible, I believe it's going to happen, that there will be a signed peace treaty by the time I leave office." He leaves office on 20 January 2009.
But beyond Iraq and the Middle East, where Mr Bush's central policy hope of greater democracy seems to have stalled, there remains the wider issue of where the US and Europe are heading.
The answer seems to be into still deep, if rather calmer, waters.
The old certainties of the Cold War have gone. And new ones have arisen, especially the antagonism of Russia, a subject Mr Bush will raise.
Dimitri K Simes, president of the Nixon Center in Washington, wrote in Foreign Affairs magazine last December: "Misguided and arrogant US policies since the end of the Cold War have fuelled resentment in Russia, and Vladimir Putin's increasing defiance is inflaming the West... Both sides must act soon to avert renewed confrontation."
This will be a major task for the new US president and for Europe.
The deterioration of relations with Russia must go down as a blot on the pages of both US and European policy makers, though of course Russia has played its own full part.
Future of EU and Nato
The European Union itself, like a lumbering behemoth, does not seem to know where it is going.
The fact is that EU governments retain the right to formulate their own foreign policies. The corollary of that is that, diplomatically, Europe as a whole punches below its economic weight. This gives the US a much freer hand as Europe is often divided.
At the end of the day, the US and Europe are still tied together by global interests, among them economics and international terrorism. Nato seems to be enduring, perhaps under the new uncertainties about Russia, though in an ideal Europe, there would be no need for it.
In the long run, a greater emphasis on a European defence policy is likely to emerge (the French will push this process during their EU presidency from July).
All this, too, will be on the new president's agenda.