Donald Trump and Kim Jong-un have become the first sitting US president and North Korean leader to meet, an unprecedented development after a year of exchanging threats.
The pair shook hands at a luxury hotel in Singapore's Sentosa island after months of diplomatic twists and turns.
They are now set to discuss defusing tensions and nuclear disarmament.
Analysts are split on what it will achieve. Some see it as propaganda win for Mr Kim, others a path to peace.
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The two men walked towards each other and firmly gripped each other's hands in front of US and North Korean flags.
In brief initial comments in front of the press, the US president predicted a "terrific relationship" with Mr Kim.
"We overcame all the odds to come here," Mr Kim said, South Korea's Yonhap news agency reports.
The leaders will now hold a one-to-one meeting, with translators, before a working lunch.
The talks - unimaginable just a few months ago - will focus on North Korea's controversial nuclear programme.
Why is this remarkable?
Last year, it would have been a rare sight to see a North Korean flag flying anywhere in Asia.
Now, Mr Kim - who runs a totalitarian regime with extreme censorship and forced-labour camps - is meeting and greeting dignitaries.
What are the talks about?
The summit will focus on North Korea's controversial nuclear programme.
US Secretary of State Mike Pompeo said the US would only accept "complete, verifiable and irreversible denuclearisation" - but would offer "unique" security guarantees.
A formal end to the Korean war may also be discussed. The 1950-53 conflict ended with a truce, not a final peace treaty. Mr Trump says signing a peace agreement would probably be "the easy part".