What are the US and EU fighting about?
The European Union says that US exporters are getting unfair help from their government.
It says that under an obscure provision of US tax laws, US companies are exempt from paying tax on the profits from their exports - all they have to do is set up "foreign sales corporations" based in overseas tax havens.
That makes it easier for Boeing, for example, to boost sales of its planes to other countries, and makes life difficult for its European rival Airbus.
Under the rules that govern the world trading system, such behaviour is illegal.
The EU raised the issue with the World Trade Organisation, the body that manages the world trading system, and mediates in trade disputes.
What happens now?
Trade disputes take a long time to resolve, and this one has been going on since 1998.
The EU has already won three rulings in the case.
But now time is on the side of the EU.
The WTO still has to approve the findings officially, but that is a formality. Once that has happened, a WTO arbitration panel will be set up, to decide on the amount of sanctions to be imposed on US exporters. It has 60 days to do the job.
The EU is claiming $4bn in damages, which it could recover through imposing an equivalent amount of tariffs on a range of US goods which are sold to European consumers.
However, there is likely to be intensive negotiation between the EU and US before this happens.
Are there other trade tensions between the US and the EU?
There are a number of outstanding trade disputes between the world's two big trading blocs.
The EU has had a long-standing ban on importing US hormone-treated beef, claiming that it is unsafe.
The WTO has repeatedly ruled against this claim, and the US is currently imposing $114m worth of sanctions against EU goods in retaliation.
The EU also is casting a wary eye on US exports of GM crops such as soya beans, which are often used in processed foods.
There has not been a formal complaint yet, but the EU made it clear at recent trade talks that it wanted to ensure that consumers had the right to clear labelling of the GM content of imported food.
There is also the matter of steel, where the US wants to limit imports from around the world on the grounds that other countries are "dumping" their excess steel production at below-market prices in the US.
The EU and other producers have said they would complain to the WTO about any steel import restrictions.
How serious could this dispute be?
This is the largest trade dispute yet that has come before the WTO, and it has the potential to cause massive disruption to trade relations.
The US, with its economy in recession, is facing increasing protectionist pressures, especially in Congress, and will be angered by sanctions that could hurt some of its most profitable companies, like GE, Boeing and Microsoft.
But the EU has been adopting an increasingly aggressive trade stance, and has the economic muscle to stand up to the US.
The world trading system is facing a series of difficult negotiations over the lifting of restrictions, after an agreement in principle in November at Doha to begin a new trade round.
If this dispute is not resolved, it would make a very bad start to the new trade round.