What are they, how has the world reacted and what are the implications for Britain and global trade?
Trump has announced big taxes on US imports of metals from the EU, Canada and Mexico
Yet China was the main target during his fiery US presidential campaign
Move draws criticism from the US's trading partners and allies
Here we explain what has happened and set out the reactions and implications
China is at the heart of Trump's strategy on global trade operations
Donald Trump's administration last night imposed new trade tariffs on steel and aluminium imports into the US from the EU, Canada and Mexico.
Yet China is the country really at the heart of Trump's decision-making strategy on trade.
During his presidential campaign, Trump accused China of flooding the global market with cheap metals, triggering job losses in the US and an 'unfair' market.
Early on, Trump vowed to impose taxes and tariffs on imports to the US from China in a bid to create a more level playing field, or, at least, one that favoured the US.
But instead it is the US's closest allies like the UK and the EU, and nearest trading partners Canada and Mexico, that are now bearing the brunt of Trump's determination to follow through on his campaign promises.
Together they exported around £17billion worth of steel and aluminium to the US in 2017, equating to nearly half of the total steel and aluminium imports.
Now, these imports will be slapped with a 25 per cent and 10 per cent tax respectively.
The tariffs will hit a wide range of products, including plated steel, slabs, coil and rolls of aluminium, all of which are used extensively within the US manufacturing, oil and construction sectors.
The new tariffs took effect at midnight on Thursday 31 May. Here we explain China's role in all this, why Trump has done it, and what a trade war will really mean.
What is China's role in all this?
China was the country that was in Trump's sights during his presidential campaign.
Yet looking at recent figures compiled by the Peterson Institute for International Economics, China made $2.9billion worth of steel and aluminium imports to the US last year.
That's a lot lower than steel and aluminium imports from Canada and the EU to the US.
Chad Brown from PIIE said: 'We don't buy steel and aluminum from China. We buy it from our allies.'
How hard has Trump's office hit China's trade network so far?
In March, the president threatened tariffs on an additional $50billion in Chinese goods later this month - although the extent and details of these have ranged backwards and forwards in announcements since.
China is also subject to the steel tariff but, as explained above, does not export much of the metal to the US so is relatively unaffected. For the moment, it seems like Trump has imposed heavier tariffs on his supposed allies than China.
Speaking as news of the original tariffs broke in March, Chad Brown from PIIE said: 'President Trump and Commerce Secretary Wilbur Ross repeatedly single out China as the principal target of the administration’s actions.
'But earlier trade restrictions already cover nearly 94 percent of US imports of steel products from China. As a result, Trump’s 25 percent tariff would have less impact on China than on other producers, many of them important security allies of Washington.'
According to an official from president Obama's era, Trump's metal tariffs announced today serve as a 'gift' for China.
'The world was aligned with the United States in recognizing China's threat around steel and aluminum', Robert Holleyman, a former deputy US trade representative, told CNBC.
He added: 'We've now turned our ally Canada into a potential ally of China on these issues. It's nonsense, it's costly, it'll hurt exporters.'
What's happening now when it comes to trade relations between the US and China?
The US is in the midst of crucial but protracted trade negotiations with China - in a bid to cut America’s $375billion trade deficit with Beijing.
Senior US officials are in Beijing preparing for a third round of high-level trade talks scheduled for Saturday. Analysts have warned of the risk of a full-blown trade war for the global economy and the markets.
While Trump risks alienating his traditional trading allies, he could be using this as a bargaining tool to justify raising further tariffs on China - as he can claim they are being treated the same as other nations.
'The Trump administration seems to regard overt threats, including tariffs and repudiation of previous agreements, as a key element for gaining leverage in trade negotiations,' said Eswar Prasad, a former head of the International Monetary Fund’s China division and now a professor at Cornell University.
Prasad warned that the United States was doing so at the cost of alienating key allies and undercutting broad international pressure on China.
Chinese foreign minister Wang Yi today said that in the dispute with the US, Beijing would 'not only try to uphold China's own interests but also uphold international rules and the global free trade system'.
Mr Wang said China will seek 'more concrete and in-depth discussions' with the US in the hope of finding a 'mutually beneficial outcome'.
'China is a responsible nation in international interactions,' he said. 'We always honour our words. That said, we also expect our partners to be keeping their words as well.'
Why has Trump done this?
Trade played a major role in Trump's presidential campaign back in 2016. During that campaign, he blamed unfair global trade deals on job losses within the US.
Since 2000, 50,000 jobs have been lost in the steel industry and 40,000 in the aluminium factories.
Speaking at a metals recycling facility in Monessen, Pennsylvania, in June 2016, Trump said: 'We tax and regulate and restrict our companies to death and then we allow foreign countries that cheat to export their goods to us tax-free. How stupid is this? How could it happen? How stupid is this?'.
He added: 'We are going to put American steel and aluminium back into the backbone of our country.'
During the speech, Trump warned he would impose taxes and tariffs on foreign countries importing their products into the US.
Before this week, what tariffs had Trump already introduced?
On 1 March, Trump announced he was introducing a 25 per cent charge on steel imports and a 10 per cent charge on aluminium imports. In total, the tariffs would have an impact on around $48billion worth of trade.
Trump was primarily taking aim at China, which had been dubbed by the president as the 'bad guy' of global trade. The tariffs were supposed to come into force the following week.
After a backlash, Trump then initially suspended the tariffs for Argentina, Australia, Brazil, South Korea, Canada, Mexico and the EU from the tariffs, pending further negotiations.
If those negotiations did not make sufficient progress in Trump's eyes, then the tariffs would be imposed at a later date. This is what has ended up happening.
US Commerce Secretary Wilbur Ross has said talks with the EU, Canada and Mexico had not made enough progress to warrant a further reprieve, meaning the geographical reach of the tariffs has been extended.
Also in March, Trump scheduled $50bn worth of tariffs on hundreds of Chinese industrial goods to come into force in June - but talks are ongoing in Beijing to avert a possible trade war (see below).
What are the implications for Britain?
Around 7 per cent of the UK's steel output, 350,000 tonnes, was exported to the US last year. For this reason, the industry fears the tariffs could cause serious damage.
The UK's steel sector remains a major employer, despite having shrunk significantly in recent decades.
The director of trade body UK Steel, Gareth Stace, said he was 'very, very worried' about the potential impact of a 'double whammy' on British producers from the Trump administration's decision.
UK steel producers could be shut out of an American market where they sold around £350million of exports last year, while also facing increased competition from a 'tsunami' of cheap steel diverted away from the US, he said.
Mr Stace told BBC Radio 4's World at One it was too early to speculate on the likely impact on jobs, but said: 'At worst, we could fall straight back into the crisis we suffered in 2015/16, which was the worst steel crisis in a generation.
'We are heading for a trade war, which is going to be all losers - there will be no winners. The US economy will suffer as much as any other economy.'
Mr Stace said the EU should activate 'safeguard measures' to prevent European markets being disrupted by a surge of as much as 25million tonnes of steel diverted from the US.
Liam Fox describes US steel tariff imposition as 'patently absurd'
Adam Marshall, Director General of the British Chambers of Commerce, said: 'It is hugely disappointing that the US government has chosen to push ahead with these tariffs, which will hurt companies and communities in many areas of the UK, as well as their customers in the US.
'The UK government must reach out to and support the many supply chain businesses that face becoming the "collateral damage" of the Trump administration’s protectionist push. British ministers must also work hand in hand with the EU to avoid any further escalation, and to find a long-term solution.
'As the UK leaves the EU, the American government’s decision to impose punitive tariffs is a helpful reminder that self-interest looms large in trade negotiations. Ministers should reflect on this carefully before they pursue any future trade deal between the UK and the USA.'
How has Britain's government reacted to the announcement?
A government spokesman said they were 'deeply disappointed' and that the UK and other EU countries, being close allies of the US, had not been 'permanently and fully exempted' from the tariffs.
He added: 'We will continue to work closely with the EU and US administration to achieve a permanent exemption, and to ensure that UK workers are protected and safeguarded.'
UK International Trade Secretary Liam Fox said the levy on steel was 'patently absurd'.
He added: 'It would be a great pity if we ended up in a tit-for-tat trade dispute with our closest allies.'
Barry Gardiner, of the Labour party, said the measures were 'based on a lie', adding the UK should not be 'bullied by the president... we believe in a rules-based system and Trump doesn't.'
The tariffs will also muddy the waters on any future trade deal with the US after Brexit.
How has the EU reacted so far?
European Commission president Jean-Claude Juncker said he plans to take the US to the World Trade Organization over the American tariffs, branding the tariffs 'totally unacceptable'.
This was later confirmed by the EU's high representative for foreign affairs, Federica Mogherini, who also flagged up additional duties on a number of American imports.
Ms Mogherini said measures being put into effect on Friday were 'reasonable, proportionate and in full compliance with WTO rules and obligations'.
While saying that 'the EU has to defend its interests', she stressed that the US remained 'our closest partners and friends and allies'.
She rejected talk of a trade 'war', telling reporters at an EU-China Strategic Dialogue meeting: 'The European Union is not at war with anyone, we don't want to be. For us that is out of the question.
'War doesn't belong to our DNA or vocabulary - we've had enough of different wars in our history, that's over. The EU is a peace project, including on trade.'
There is a 10-page list of tariffs on US goods ranging from Harley-Davidson motorcycles to food goods.
French president Emmanuel Macron has branded the move from the US 'illegal'.
What is the reaction from Canada and Mexico?
Canadian prime minister Justin Trudeau said the US's move was 'totally unacceptable' and rejected the claim that his country posed a national security threat to America.
In response, Canada plans to impose tariffs of up to 25 per cent on roughly $13billion worth of US exports from 1 July.
Mexican Foreign Minister Luis Videgaray said his country was planning new duties for imports of steel, pork, apples, grapes, blueberries and cheese from the US.
Canada announces retaliatory tariffs against US exports
What has been the reaction in the US?
'Europe, Canada & Mexico aren't China. You don’t treat allies the same way you treat opponents. Blanket protectionism is a big part of why we had a Great Depression. "Make America Great Again" shouldn’t mean "Make America 1929 Again." ' tweeted Republican Senator Ben Sasse, joining an opposition that included many Republican officials and business groups.
U.S. Chamber of Commerce President Tom Donohue warned in a letter to the body’s board that current trade policies could threaten economic progress and cause the loss of more than 2 million jobs, mostly in states that voted for Trump.
How have the markets reacted?
With fears over a potential trade war looming large, in the immediate aftermath of the announcement, the Dow Jones dipped by around 1 per cent. But European markets widely shrugged off the announcement today - buoyed by progress in Rome on forming an Italian government.
The FTSE 100 is 0.6 per cent up, while the leading French and German stock market indices are mo