The only words we can say are “thank you”, PM Theresa May has told veterans at a ceremony marking 75 years since the Allied invasion of Normandy during World War Two.
French President Emmanuel Macron also addressed D-Day veterans gathered for the anniversary in northern France, saying “our freedom” was owed to them.
Events began with a lone piper marking the moment UK soldiers went ashore.
Donald Trump also spoke to US veterans, calling them “the pride of the nation”.
Hundreds of veterans have visited France for the anniversary of the D-Day landings – the largest combined land, air and naval operation in history.
The day’s commemorations marked key events from the wartime operation, which represented the start of the campaign to liberate Nazi-occupied north-west Europe.
By nightfall on 6 June 1944, some 156,000 Allied troops – including British, US and Canadian forces – had landed on Normandy’s beaches, despite challenging weather and fierce German defences.
Some had drowned when they were accidentally dropped off too soon in deep waters.
By the end of D-Day, the Allies had established a foothold in France and within 11 months Nazi Germany was defeated and the war was over.
At 06:26 BST – the exact minute the first British troops landed on the beaches in 1944 – a lone piper played on a section of the Mulberry Harbour in the French town of Arromanches.
Mr Macron and Mrs May – in one of her final engagements as Conservative leader – were in Ver-sur-Mer to see the first stone laid for a memorial to commemorate the 22,442 British troops who died there in the summer of 1944.
The memorial, which overlooks Gold Beach, depicts three soldiers advancing across the sand.
Mrs May said she was humbled to be able to mark the moment with veterans, who belonged to a “very special generation”.
“A generation whose unconquerable spirit shaped the post-war world. They didn’t boast. They didn’t fuss. They served,” she said.
“And they laid down their lives so that we might have a better life and build a better world.
“If one day can be said to have determined the fate of generations to come in France, in Britain, in Europe and the world, that day was 6 June 1944,” she added.
Also paying tribute, Mr Macron said: “This is where young men, many of whom had never set foot on French soil, landed at dawn under German fire, risking their lives while fighting their way up the beach, which was littered with obstacles and mines.”
The French president also went on to say he was proud to have worked with Mrs May.
“Leaders may come and go but their achievements remain. The force of our friendship will outlast current events,” he said.
Following the inauguration ceremony, Mrs May, the Prince of Wales, the Duchess of Cornwall, Labour leader Jeremy Corbyn and Scotland’s First Minister Nicola Sturgeon attended a service at the cathedral in Bayeux, the first city to be liberated by the invasion.
At the start of the service, a message was read out on behalf of Pope Francis, in which he said D-Day was “decisive in the fight against Nazi barbarism”. He also paid tribute to those who “joined the Army and gave their lives for freedom and peace”.
Labour leader Jeremy Corbyn said the service was “beautiful and inclusive”, in memory of those “who died in Normandy and ultimately helped to defeat the scourge of fascism”.
The service was followed by a ceremony at Bayeux War Cemetery, where many of the fallen are buried.
Meanwhile, Mr Trump accompanied Mr Macron at a ceremony at the US war cemetery at Omaha Beach, Colleville-sur-Mer.
He told veterans gathered there: “You are among the greatest Americans who will ever live. You are the pride of the nation. You are the glory of our republic and we thank you from the bottom of our hearts.”
At the National Memorial Arboretum, the Duke of Cambridge gave an address which was originally made by his great-grandfather, George VI in 1944.
He read: “Four years ago our nation and empire stood alone against an overwhelming enemy, with our backs to the wall.
“Now, once more, a supreme test has to be faced.”
He added: “This time, the challenge is not to fight to survive but to fight to win the final victory for the good cause.
“At this historic moment, surely not one of us is too busy, too young, or too old to play a part in a nationwide, perchance a world-wide, vigil of prayer as the great crusade sets forth.”
During Prince Harry’s visit to Royal Hospital Chelsea, he joked with Chelsea Pensioners and asked them “Who’s your favourite?” while gesturing to hospital staff.
On Wednesday, leaders from every country that fought alongside the UK on D-Day joined the Queen in Portsmouth for the first day of the 75th-anniversary events.
The Queen paid tribute to the “heroism, courage and sacrifice” of those who died.
Around 300 veterans were then waved off on the cruise ship MV Boudicca as it set off for the Normandy commemorations.
Two veterans – Harry Read, 95, and John Hutton, 94, – parachuted back into Normandy, 75 years after their first landing.
This time, they jumped in tandem with members of the Army’s Parachute Regiment display team, the Red Devils – and were greeted by cheers.BBCnews