She has a reputation as being cool and conservative, the former physicist who leads Europe's strongest economy.

He's the wealthy real estate magnate known from shooting from the hip, the president of the world's biggest superpower.

And when German Chancellor Angela Merkel meets Donald Trump for the first time in Washington today it may be the American's most important state visit yet.

For months, the two have been testing the countries' relationship over differences in policy and values.

Merkel is said to have studied meticulously ahead of the trip.

German officials say she's pored over Trump's speeches and interviews, even as far back as a 1990 interview with Playboy.

Where he laid out many opinions that would carry through to the Oval Office.

She's also analysed his recent encounters with other leaders from Britain, Canada, and Japan.

One German official telling Reuters that Merkel's been coached on the idea that Trump prefers to hear "clear positions" but with "few details".

They also said he doesn't like to listen to long conversations.

But Trump is also expected to seek her advice.

She's been chancellor for over a decade - making Trump her third US President.

And the White House has said Trump will pick her brain on how to deal with the sensitive diplomacy of another leader, Russian President Vladimir Putin.

There's a lot more riding on the meeting.

They've stood at odds on immigration and trade, the role of the European Union, and other issues.

When he was a candidate, Trump said Merkel was "ruining Germany".

If nothing else, today should see some warmer language.