What impact will the tariffs have on world steel exporters?
Some of them fear that they will make it impossible for them to sell steel in the US.
Exports to the US account for about five percent of European Union steel production. The EU is particularly concerned that Asian steel may be diverted to the European market.
Will the move backfire on other US industries by making steel more expensive?
Many American steel using companies industries are opposed to the tariffs. The lobby group, Consuming Industries Trade Action Coalition, says the tariffs will cost more jobs in industries that use steel than they will save.
They say that for example many car parts now made in the US will be made abroad.
The steel producers reject this. The American Iron and Steel Institute says the effect on consumers prices will be minimal and there will be no meaningful employment costs for steel using industries.
What are the domestic political calculations behind President Bush's move?
There are elections for the House of Representatives in November this year. The House is finely balanced and steel-producing areas such as Ohio and Pennsylvania could determine whether the Republicans retain control of the House.
It might also be an important issue in the Presidential election in 2004.
George W Bush came to power after promising to help the steel industry. He narrowly won the election of 2000, after winning two states, Ohio and West Virginia, where the steel industry has a large presence.
Is it true that the US has been too slow in restructuring its steel industry?
The industry says no. It claims to be the most efficient and least protected steel in the world. There have been 30 bankruptcies in the sector in the last five years or so.
It blames the problem of excess global capacity in the steel industry on government subsidies abroad.
The critics of the US steel industry say it needs to bite the bullet and slim down. It is in trouble, they say, because its costs are too high.
What can the rest of the world do about it?
In the first instance complain to the World Trade Organisation.
The US is using a procedure known as safeguards under which countries can impose import restrictions to give temporary protection to an industry that has suffered serious injury as a result of a surge in imports.
A complaint to the WTO would have to argue that the investigation by the US International Trade Commission - which is the basis for President Bush's decision - had failed to show that.
A spokesman for the European steel lobby group says a complaint on that basis would be "an easy win".
EU officials have also said they would consider a safeguard action of their own.
The problem with using WTO procedures is that they are slow.
The rest of the world could consider slapping tariffs on US goods, although that would not normally be consistent with WTO rules, unless there has first been permission given by a WTO dispute settlement panel.
Is this about unfair imports into the US?
Not strictly, no. Under the safeguard provisions of the WTO, there is no need to demonstrate unfairness.
However, the US industry does say that most of the imports that have done them so much damage are in breach of other WTO rules: they are either subsidised by foreign governments, or are dumped, that is sold in the US for less than the price in the country of origin.
The US has take a number of actions against these problems which are directed against specific countries.
But steel producers say that the unfair imports keep coming from other sources. So they wanted a global solution to protect them from all imports.
What other disputes are current between the EU and the Americans?
The WTO upheld a complaint from the EU made in 1997 that a provision in US tax law was in effect a subsidy for exports, which is banned under WTO rules.
The US changed its laws but the WTO again supported the EU in saying that the changes weren't enough. The EU is waiting for a WTO ruling on what sanctions or retaliatory tariffs it can impose on US goods.
The US won a case against the EU on Europe's ban on imports of beef treated with growth promoting hormones.
The EU refused to comply with the ruling and US sanctions on some EU goods are still in place. The two sides are negotiating.
The solution is likely to involve compensation for US farmers and a quota of beef imports - hormone free - earmarked for the US.