US President Barack Obama has cancelled plans to station an anti-ballistic missile system in Poland and the Czech Republic.
Former US President George W Bush had signed deals to base interceptor missiles in Poland and a radar in the Czech Republic.
President Bush planned it as part of a missile defence shield to counter what it described as threats from rogue states such as Iran. But a furious Russia objected.
President Obama now says that any threat from Iran can be countered by shorter-range systems.
What was the US proposing to do?
The US has been developing a missile defence system intended to destroy incoming ballistic missiles potentially coming from North Korea and Iran.
This involves using radars in Alaska and California in the US and at Fylingdales in the UK. Another radar is planned for Greenland.
Anti-missile missiles, or interceptors, are being based in Alaska (40 of them) and California (four).
There would also be 130 interceptors based on ships. The interceptors work by physically hitting the ballistic missile in mid-flight. There would also be missiles to try to destroy incoming rockets in the final stages.
However, the US also planned to install 10 more interceptors in silos in Poland, and build a radar station in the Czech Republic.
It envisaged that construction of the Czech facility - using a radar currently located at Kwajalein Atoll in the Marshall Islands - could begin next year, with the first interceptors in place in Poland by 2011 and the system fully operational by 2012.
Why in Eastern Europe?
The US says there was a gap in its anti-missile defences.
A threat from North Korea could be countered with the US and sea-based systems.
But European allies or US forces in Europe could be threatened by Iran one day, Washington said, or indeed some other country, so there needed to be a system based in Europe as well.
So why has President Obama abandoned the European project?
As soon as he came into office in January, he launched a review and he is now acting on the recommendations of that review. He says that US intelligence assesses that Iran has not concentrated on long-range ballistic missiles as much as had been expected but on shorter-range ones instead.
Therefore, the argument is, there is now no need for the European deployment. Instead, different ship and land-based systems closer to Iran will be used instead to counter any potential threat to Europe.
Why did Russia object to the Polish and Czech deployment?
Moscow said that the anti-missile missiles in Poland and the radar in the Czech Republic could threaten its own defences. The system might be small to start with, it said, but could expand. The radar could be used to spy on Russia.
Russian President Dmitry Medvedev warned that "we will not be hysterical about this, but we will think of retaliatory steps".
The Pentagon said this was just "bellicose rhetoric" from Russia "designed to make Europeans nervous".
Has President Obama given in to the Russians?
He says not and that he is simply reacting to a change in threat perception. However, the Russians are delighted as they see this as a diplomatic and military victory.
The president's critics at home and abroad accuse him of making an unnecessary concessions that will encourage further hardline Russian positions.
Does this mean the whole anti-missile system will be dismantled?
No. Other parts of the system are still planned. But perhaps more emphasis in future will be put on the ship-based interceptors that are more mobile.
Will the system work?
The theory is that the interceptor missile homes in on and destroys its target in the air by physically hitting the incoming warhead.
However, the closing speed of interceptor and target will be 24,000kph (14,900mph), or 6.5km (4 miles) per second - so the task is more difficult than hitting a bullet with another bullet.
The system's supporters say that not only does it work, but it is even more accurate than that.
But critics say that, despite having spent over $100bn (£54bn), the Pentagon still has not proved the system can work in realistic conditions.
Independent scientific bodies in the US have said that tests of the system's intercept capabilities have been highly scripted, with the defence being given detailed information about the attack beforehand.
They also argue that the defence system could be easily circumvented by potential attackers.
What international agreements cover these moves?
None. The US withdrew from the Anti-Ballistic Missile Treaty in 2001.
This treaty limited US and Soviet anti-missile defences to one site each. The Russians still operate theirs, around Moscow.
The US chose to defend its strategic rockets in North Dakota but this defence has been deactivated.
Part of the Russian unhappiness about the Europe sector of the anti-missile system is that it results from the US withdrawal from the ABM treaty and Russia is worried about where it might go next.
Russia has announced the testing of a new multiple-warhead missile, the RS-24, which it says is designed to overcome missile defences. It is also developing new cruise missiles.
What ballistic missiles do the US and Russia have?
They have dramatically reduced their arsenals from the Cold War days but still retain substantial forces of several thousand missiles and nuclear warheads each.
Under the Strategic Offensive Reductions Treaty (SORT) signed by presidents Bush and Putin in 2002, each side has to reduce its deployed warheads to a maximum of 2,200 by 2012.
The two sides have agreed to try to reach a new agreement by the end of 2009.
Russia has its own radar early warning system, short-range interceptor missiles in bases around Moscow and a number of land-based Intercontinental Ballistic Missile launch sites across the country.