As the two leaders prepare for the key meeting on 12 June, we look at the details of the summit and the goals of both sides.
The summit starts on the morning of 12 June at the Capella Hotel on the Singaporean resort island of Sentosa.
A win for the US president would involve the North Korean leader agreeing to shut down his nuclear weapons programme.
A headline-grabbing made-for-TV moment on the world stage would also be welcomed by the former reality TV star.
There are concerns that he may leave out human rights issues (North Koreans live under one of the world's most oppressive regimes) and regional security concerns (such as what is best for South Korea and Japan) but he has said more than one meeting may be needed to achieve what he wants.