Holocaust survivors and international leaders are honouring victims of the Nazis at the former Auschwitz death camp, amid calls to fight resurgent anti-Semitism.
The presidents of Israel and Poland - Reuven Rivlin and Andrzej Duda - laid wreaths together, 75 years after Soviet troops liberated the camp.
About 1.1 million people, mostly Jews, were murdered at Auschwitz-Birkenau.
Mr Rivlin warned of "voices which spread hate" and threaten democracy.
"Our duty is to fight anti-Semitism, racism and fascist nostalgia - those sick evils," he said.
He and President Duda laid wreaths at the Death Wall, where the Nazis shot thousands of prisoners.
The vast Auschwitz-Birkenau camp complex, in Nazi-occupied southern Poland, was the regime's most notorious killing centre.
Thousands of Poles, Soviet prisoners of war, Gypsies (Roma) and other persecuted groups also died there.
Nazi Germany murdered about six million Jews in its campaign to dominate other races and nations.
This may be the last major anniversary where so many survivors are able to attend.
There is widespread concern about high levels of anti-Semitic intimidation and violence in several countries and the proliferation of hate speech on the internet.
In Paris, French President Emmanuel Macron spoke at a ceremony to mark the 75th anniversary, including additions to a wall of remembrance for 77,000 Jews deported to concentration camps from France.
The Shoah Memorial was renovated, with 175 extra names and 1,498 more birth dates added after research in Holocaust archives.
"The return of this anti-Semitism is not just a problem for Jews. It is a problem for all of us. It is the Republic's problem," President Macron said.
More than 200 survivors travelled to Auschwitz from across the globe to mark the 75th anniversary. Many wore blue-and-white scarves - a reminder of the striped prison uniforms that victims wore in the concentration camps.
A woman who was born in the camp a few months before liberation, 75-year-old Jadwiga Wakulska, said "my mother was holding me in her arms as a four-month-old child, as she was standing in line to the gas chamber...
"We were coming closer and closer to the gas block and one of the Germans saw me. He looked at me and since I was a blonde baby with blue eyes he took me aside and told me I will survive. Thanks to that we survived. My mum says that thanks to the fact that I had a Nordic appearance, I saved her and myself."