The bilateral meeting tomorrow comes as both leaders face tough challenges on the world stage, with May stumbling through the Brexit process and several of Trump's aides under investigation for possible ties with Russia.
The G20 in Germany will likely be dominated by North Korea's testing of an intercontinental ballistic missile which could reach the US, prompting Trump to declare he had run out of "patience" with the Pyongyang regime.
On the eve of the summit he will meet with German Chancellor Angela Merkel, while Friday will see Trump hold talks with Russian President Vladimir Putin.
Trump's second foreign tour follows his visit to Italy in May for the G7 summit, during which he clashed with other leaders on climate change.
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He has found a cautious ally in Britain's leader, who hotfooted to Washington just days after Trump was elected in the hope she could secure the promise of future trade ties once the UK leaves the European Union.
But the visit received huge criticism at home, with a petition against May's offer to Trump of a state visit to London attracting more than 1.8 million signatures.