US President Donald Trump and First Lady Melania Trump have met the Queen on the first day of their state visit to the UK.
The pair went to Buckingham Palace for a private lunch and welcome ceremony.
Mr and Mrs Trump laid a wreath at the tomb of the unknown warrior in Westminster Abbey and are due to attend a state banquet this evening.
Minutes before arriving in the UK, Mr Trump criticised the Mayor of London, with whom he has clashed in the past.
He tweeted that Sadiq Khan - who had earlier said the UK should "not roll out the red carpet" for Mr Trump - was a "stone cold loser", but the president added he was looking forward to his visit.
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, before travelling to Buckingham Palace.
Protests are planned in several UK cities during the three-day visit, including in London, Manchester, Belfast, and Birmingham.
Labour leader Jeremy Corbyn - who is boycotting the state dinner - is due to attend and speak at the London demonstration, a party spokesman has confirmed.
Earlier, Mr Corbyn tweeted: "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."
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.
The president's visit coincides with the commemorations for the 75th anniversary of the D-Day landings, which the Queen, Mr Trump and other heads of state will attend at Portsmouth on Wednesday.
Crowds were gathered outside Buckingham Palace as the president and first lady landed by helicopter shortly after midday.
The Queen presented Mr Trump with a first edition of Sir Winston Churchill's book The Second World War, from 1959, with gilt decorations and hand-sewn bindings in the colours of the US flag. He was also given a three-piece Duofold pen set decorated with an EIIR emblem, in a design made exclusively for the monarch.
Mrs Trump received a specially commissioned silver box with a handcrafted enamel lid, decorated in royal blue with roses, thistles and shamrocks to represent the ceiling of Buckingham Palace's music room.
After the private lunch, the Queen showed the couple American artefacts and other items from the Royal Collection. In a nod to the US leader's Scottish heritage, he was shown a bolt of Harris tweed.
Mr and Mrs Trump met the Duke of York at Westminster Abbey, where they laid a wreath at the grave of the unknown warrior. The president signed the distinguished visitor's book in his customary black marker pen, describing the 13th Century church as a "special place".
Their next stop was Clarence House, where they joined Prince Charles and the Duchess of Cornwall for tea.
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.
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."
Mr Khan was not the only target of the president's tweets. Mr Trump also criticised CNN, complaining that it was the primary source of news from the US on his trip - but that he had to turn off its "fake news" after a short while.
China, which is in an ongoing trade dispute with the US, also came under fire. Mr Trump claimed that companies are leaving China in order to avoid paying the tariffs and that the US is "taking billions".
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.