The Queen has met Pope Francis for the first time, during a one-day visit to the Italian capital, Rome.
The meeting in the Vatican was described as a private one and pomp and protocol were kept to a minimum.
Earlier, the Queen and Prince Philip had lunch with the Italian President, Giorgio Napolitano, and his wife Clio at the Quirinal Palace.
The Queen gave the Pontiff a hamper of British produce and received a lapis lazuli orb for baby Prince George.
It is the Queen's first foreign trip since a visit to Australia in 2011.
Arriving at the Vatican, the Queen shook hands with the Pope and said "Sorry to keep you waiting, we were having lunch with the president."
The Queen and Prince Philip later had tea with the Pope in a suite of rooms in the Pope Paul VI Audience Hall, close to the Casa Santa Marta, the guest house in the Vatican where the Pope has chosen to live.
It is her third visit to the Vatican during her reign but the first time she has met Pope Francis, who was installed just over a year ago.
In a break with Vatican convention, the Queen did not wear black, or a veil, but instead wore a lilac-coloured spring coat and matching hat.
The Queen and the Pope exchanged gifts inside the Vatican. Pope Francis gave the Queen a royal orb made of lapis lazuli with a silver cross on top, for her baby great-grandson Prince George.
The orb is an emblem of royal power which the ancient Romans used to represent the universe, before it was adapted by Christians who added a cross on top to represent the world under Christianity.
The Queen presented the pontiff with a hamper of British produce, including goods grown in the gardens of royal palaces, and whisky.
The Queen, who is supreme governor of the Church of England, met the leader of the world's Roman Catholics at a time of thorny Anglican-Catholic relations over the Vatican's move to bring in hundreds of Church of England priests dissenting from their Church's line on the ordination of women.
Relations between the Archbishop of Canterbury Justin Welby and Pope Francis are cordial, however and the Queen has long supported moves to improve understanding between the Anglican and Roman Catholic churches, BBC correspondents say.
One subject that was not expected to be discussed was the Falkland Islands, known in Argentina as Las Malvinas, which are controlled by the UK but claimed by the Pope's native Argentina. He has in the past referred to the islands as "ours".
The visit coincides with the 32nd anniversary of the start of the Falklands War.
Speaking to Vatican radio, Britain's ambassador to the Holy See, Nigel Baker, said: "The Vatican has been clear with us, including in the last week and at a very senior level, that their long-standing position of neutrality on this issue remains in force."
He added that the Queen "will want, I think, to understand from Pope Francis how he sees the role of faith in the world".
Queen Elizabeth II had previously visited the Vatican three times during her reign - once to meet John XXIII in 1961 and again in 1980 and 2000 to see John Paul II, whom she also met at Buckingham Palace in 1982.
Both former popes are being made saints in a first-ever double papal canonisation later this month.
The Queen also met Pope Pius XII in 1951 - a year before she took the throne - and the now pope emeritus Benedict XVI in Edinburgh when he visited the UK in 2010.
The Anglican church, which separated from Rome after the divorce of King Henry VIII in the 16th Century, has about 80 million followers compared with the world's 1.2 billion Catholics.