Events have been taking place to mark Holocaust Memorial Day in memory of the six million Jews and other victims of the Nazi death camps.
Most of the commemorations take place on 27 January - the date on which the Auschwitz concentration camp was liberated by the Soviets in 1945.
Victims of more recent atrocities are also being remembered.
On the eve of the memorial, the UN General Assembly on Friday adopted a resolution condemning Holocaust denial.
The resolution, proposed by the United States and co-sponsored by more than 100 countries, says "ignoring the historical fact of these terrible events increases the risk they will be repeated".
The resolution does not mention any particular country, but diplomats said it was aimed at Iran, which has cast doubt on the Nazi genocide of Jews during World War ll.
'Dignity of Difference'
Two years ago, the UN designated 27 January as the date for international commemorations.
Events this year included a ceremony at the former concentration camp of Sachsenhausen in Germany.
There was also a wreath-laying ceremony on Berlin's Putlitz Bridge, where there is a plaque commemorating the deportation of the city's Jewish community during the Nazi regime.
The bridge has been targeted in the past by far-right groups.
At Saturday's ceremony, the head of the Green Party, Claudia Roth, said: "We all have a responsibility to combat anti-Semitic and far-right attitudes."
It was a view echoed by German Chancellor Angela Merkel, who urged "all courageous democrats" to fight against the far-right NPD party, which is represented in regional parliaments.
On Saturday evening, hundreds of people attended a concert at Berlin Cathedral. The proceeds will go to a group that provides counselling and support for survivors of the Holocaust living in Israel.
Events have been organised in the UK with the message "The Dignity of Difference" and with the aim of educating people about the dangers of anti-Semitism, racism and all forms of discrimination.
The victims of other atrocities of the 20th Century, including in Cambodia, Rwanda, Bosnia and Kosovo, are also being honoured.
Some six million Jews were killed during the Holocaust - the attempt by Nazi Germany to exterminate Europe's Jewish population during World War ll.
The Nazis also targeted other groups who were seen by them as racially inferior or degenerate, including Slavs, Roma, homosexuals and disabled people.
It is estimated that about 1.5m people were killed at Auschwitz, the biggest of the concentration camps.
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