US President Donald Trump and First Lady Melania Trump are meeting the Queen on the first day of their state visit to the UK.
The pair are at Buckingham Palace for a private lunch and welcome ceremony.
Mr and Mrs Trump arrived on Air Force One earlier on Monday and were taken to the US ambassador’s home in central London, where they are staying.
Minutes before touching down, Mr Trump criticised Mayor of London Sadiq Khan, with whom he has clashed in the past.
Protests are planned in several UK cities during the three-day visit, including London, Manchester, Belfast, and Birmingham.
Talks between Mr Trump and outgoing Prime Minister Theresa May will begin on Tuesday, with the pair expected to discuss climate change and Chinese technology firm Huawei.
Crowds were gathered outside Buckingham Palace as the president and first lady landed by helicopter shortly after midday.
After a private lunch, the couple will be given a tour of Westminster Abbey and will also join Prince Charles and the Duchess of Cornwall for tea at Clarence House.
Later, the Queen will host a state banquet at Buckingham Palace, also attended by the Duke and Duchess of Cambridge.
The Duchess of Sussex will not attend following the birth of her son Archie, who is less than a month old. On Sunday, Mr Trump denied calling the duchess “nasty”, despite him using the word on tape.
As he stepped onto UK soil, Mr Trump was greeted by US Ambassador to the UK Woody Johnson and Foreign Secretary Jeremy Hunt.
Tory leadership candidate Mr Hunt, who has spoken about the importance of the UK’s relationship with the US, said Mr Trump mentioned to him “some of his very strong views about the Mayor of London” which he had also tweeted.
By James Landale, BBC diplomatic correspondent
The contrast could not have been starker. The President of the United States received a warm welcome from the Queen and the Prince of Wales at Buckingham Palace, a 41-gun salute and an honour guard of young Grenadiers resplendent in scarlet.
At the same time Mr Trump launched a verbal attack on the mayor of the city in which he is now a guest, calling Sadiq Khan “a stone cold loser” for questioning why the President had been granted a state visit.
In truth, this is all of a piece for Mr Trump: he gets the pictures and the pageantry that he wants and will look good in his re-election campaign next year, and he gets to pick a fight with a liberal, Muslim politician that will play well with his base.
Already this row is forcing those campaigning to be Britain’s prime minister to define themselves against Mr Trump.
Foreign Secretary Jeremy Hunt criticised Mr Khan for his “great discourtesy”. But Heath Secretary Matt Hancock said the office of the Mayor of London should be respected in the same way one respects the office of the president.
This visit has only just begun and already the Great Disruptor is tweeting angry thoughts and breaching diplomatic niceties. Business as usual, you might think – only today he also happens to be a guest of the Queen, who rarely tweets and is always diplomatic.
Mr Trump’s tweet accused Mr Khan of doing a “terrible job” as mayor, adding: “[He] has been foolishly “nasty” to the visiting president of the United States, by far the most important ally of the United Kingdom. He is a stone cold loser who should focus on crime in London, not me.”
A spokesman for Mr Khan said “childish insults” should be beneath the US president, adding: “Sadiq is representing the progressive values of London and our country, warning that Donald Trump is the most egregious example of a growing far-right threat around the globe.”
Labour leader Jeremy Corbyn defended Mr Khan, tweeting: “Tomorrow’s protest against Donald Trump’s state visit is an opportunity to stand in solidarity with those he’s attacked in America, around the world and in our own country – including, just this morning, Sadiq Khan.”
Although Mr Trump has spoken of his admiration for Mrs May, there are expected to be differences of opinion during their talks, which begin on Tuesday.
The prime minister will raise the issue of climate change, with a government spokesman again saying on Monday the UK was “disappointed by the US decision to withdraw from the Paris Agreement in 2017”.
The two leaders are also expected to discuss Huawei. The US has blacklisted the Chinese firm for security reasons, while the UK may allow it to supply “non-core” components for its 5G network.
Before the visit, President Trump told the Sun newspaper he was backing Conservative Party leadership contender Boris Johnson to be the next UK prime minister.
He also told the Sunday Times that Brexit Party leader Nigel Farage – an arch critic of Mrs May – should be involved in the government’s negotiations to leave the EU.
At Monday evening’s Buckingham Palace banquet, both the president and the Queen are expected to make a speech to guests, who will include prominent Americans living in Britain.
Mr Corbyn, House of Commons Speaker John Bercow, and Liberal Democrat leader Sir Vince Cable are all boycotting the state banquet.
Fans and critics outside Buckingham Palace
By Hamish Mackay, BBC News, outside Buckingham Palace
Much has been made of the the US president’s high-tech limousine – known as The Beast – but it was in the Marine One helicopter that Donald Trump made his grand arrival at Buckingham Palace.
A quick walk around the crowd outside the palace revealed the presence of supporters and detractors of Mr Trump – both equally strong in their views.
Phillip Butah, from Essex, wearing a MAGA hat and describing himself and his companion as “Trump activists”, says: “We are so happy that he’s here – this visit is long overdue.”
Asked what they expect the UK to get from this visit, they reply: “Trade deals”.
Corey Wright, a 25-year-old American from Ohio, in London as a tourist, sees the visit in a similar light.
“I think the visit is good for the political environment,” he says. “I think that needs to be worked on and that’s what he’s here to do.”
Auriel Granville – a climate activist from Wimbledon, south-west London, came dressed as the Statue of Liberty to protest against the president’s visit.
“I don’t think he should be received in this way – climate change should be top of our agenda and Donald Trump is a climate change denier.
“He’s not listening to scientists, who are all saying it is a result of human activity.
“We have a wonderful oasis of life on earth and we need to preserve it.”
Mr Trump’s daughter, Ivanka, arrived in the UK before the president. On Sunday, she posted a picture from outside the Victoria and Albert Museum in west London where she had visited the Christian Dior exhibition.
On Tuesday morning, President Trump and Mrs May will host a business breakfast at St James’s Palace.
President Trump will then visit Downing Street for further talks with Mrs May, followed by a joint press conference.
Protesters are organising a “national demonstration” which will start at Trafalgar Square at 11:00 on Tuesday.
The Met Police said it had “a very experienced command team” leading the operation to deal with the visit.
The police operation for the president’s visit last year was estimated to have cost nearly £18m.
On Wednesday, President Trump will visit Portsmouth to mark the 75th anniversary of the D-Day landings.
Although the Queen has met 12 of the 13 US presidents who have been in office during her reign, Mr Trump’s state visit to the UK is only the third by a US leader.
George W Bush and Barack Obama are the only other US presidents to be given a state visit.
State visits differ from official visits and are normally at the invitation of the Queen, who acts on advice from the government. The Queen usually receives one or two heads of state per year and has hosted 112 of these visits since becoming monarch in 1952.