President Barack Obama has had lunch with the Queen - and presented her with a photo album of the monarch's many meetings with US presidents and first ladies.
What else can you give to the woman who has everything?
The royals get all kinds of bizarre gifts, says royal historian Kate Williams.
"They get everything. People just send stuff to the Queen. They get milk bottles, they get bits of old cake, they get biscuits. They think she looks a bit hungry, so they send her some cake.
"I think the Queen would be quite partial to a box of chocolates and to put her feet up.
"Historically, the Queen prefers cheap presents. At Christmas, whoopee cushions, novelty bath hats, that kind of thing. No expensive presents at Christmas, that's where Princess Diana fell foul.
"She bought cashmere jumpers, and it was a big mistake."
Perhaps aware of Princess Diana's difficulty, the Duchess of Cambridge admitted she was stuck for ideas for her grandmother-in-law before her first Christmas at Sandringham.
In the end, she opted for a jar of homemade chutney.
"I was worried what to give the Queen as her Christmas present. I was thinking, 'Gosh, what should I give her?'" she said in her first solo television interview.
"And I thought back to what would I give my own grandparents. And I thought, 'I'll make her something'. Which could have gone horribly wrong. But I decided to make my granny's recipe of chutney.
"I was slightly worried about it, but I noticed the next day that it was on the table. I've noticed since she's done that on lots of occasions and I think it just shows her thoughtfulness, really, and her care in looking after everybody."
Meanwhile, Chinese President Xi Jinping chose to show off his family's talents by giving Her Majesty two CD sets of music starring his wife, Madame Peng Liyuan.
There was some criticism in the British press in 2009 when it emerged that Barack Obama had given the Queen a gift of an iPod loaded with some of his speeches and pictures of his inauguration.
There were also raised eyebrows when the president gave the former UK prime minister, Gordon Brown, a DVD box set of classic American films - reportedly coded for viewing only in the US.
First Lady Michelle Obama has done better than her husband. On her last visit to London, she gave the Queen silver - a Tiffany sterling silver honeycomb and bee bud vase.
She also brought a gift box containing lemon verbena tea, a candle, two small pots of honey and a jar of honey butter from the White House kitchen garden.
According to official rules, the Royal Family does not actually own the presents it receives.
Officially they belong to the whole country and are looked after by the Royal Collection.
Live animals are donated to London Zoo, and perishable items worth under £150, such as food and flowers, can be given to charities or staff.
Although, the royals can eat any food they receive.
Perhaps that was what German President Joachim Gauck was thinking when he gave the Queen a marzipan model of a Berlin monument, the Brandenburg Gate.
It is not known whether the Queen in fact demolished the marzipan monument.
Bag of salt
Last year, the Queen was given a bag of salt by the governor of the British Virgin Islands.
The 1lb bag was traditionally given to the British monarch as rent - rather than a present - for Salt Island, one of the islands in the Caribbean archipelago.
The custom dates back to the days of Queen Victoria when salt was harvested on the island, but had fallen away until it was resurrected by the governor John Duncan in 2015.
This year, the islands held a special "salt-breaking ceremony" in honour of the Queen's 90th birthday.
Fairy dust and mangoes
The official list of gifts given to members of the Royal Family, which is released every year, could be used as inspiration for anyone needing to come up with a present.
Last year's list revealed some bizarre offerings from world leaders, sports stars, and general well-wishers.
Prince Charles got a packet of fairy dust when he visited New Zealand in November, and a lot of dates - 32 packets and two buckets - and a pot of churned butter from Saudi Arabia.
Prince George got a huge haul of presents in 2014, which included a possum-skin cloak from his trip to Australia and New Zealand.
That year, Princess Anne got a box of 100 mangoes from President Mamnoon Hussain of Pakistan.
Prince Andrew got a model of a surface-to-air missile from MBDA Systems. The Duke of Kent received gifts including a picture of a washing machine.
If in doubt, diamonds
Of course it's not all fairy dust and whoopee cushions. The official gift lists show the Queen receives plenty of precious items too.
Amongst gifts to the Queen last year, for example, was a sapphire and diamond brooch in the shape of a fern from the president of Sri Lanka.
Jewellery was also what Prince Philip gave his bride on their wedding day. He designed her engagement ring, made of 11 diamonds, and her wedding gift bracelet, himself.