Besides the striking differences in their personalities, the trained German physicist with a deliberative approach and the brash US billionaire known for his Twitter outbursts also have contrasting views and stances on policies.
Setting the tone in her first phone call with Trump after he took office, Merkel offered co-operation, but also reminded him of democratic values.
That unusual warning led some commentators to suggest she had taken on the mantle of the “leader of the free world”, a title usually reserved for US presidents.
Since then, Trump has repeatedly ripped into Germany for failing to pay its “fair share” for transatlantic defence.
He has also lashed out against Germany’s vital export industry which he claims is harming US producers.
The fraught ties and Trump’s decision to withdraw the US from the 2015 Paris climate accord led Merkel to draw the startling conclusion that the US may no longer be a reliable partner for Germany and the European Union.
Europe must step up as a player in world affairs, Merkel said in 2017, signalling that the EU needs to take control of its destiny in the Trump era.