As US president Donald Trump began his second term in January, Mexico loomed large in his crosshairs.

Thousands of migrants a month were crossing the US border illegally from Mexico. Mexican cartels were smuggling huge quantities of the lethal drug fentanyl into American cities. And the country had elected a leftwing nationalist who vowed to stand up to the Americans – just the kind of politician to raise Trump’s hackles.

Yet as Claudia Sheinbaum completes a year in office, Mexico’s first woman president has surprised many. Instead of confronting Trump, she has embraced dialogue – 14 telephone conversations so far – and won concessions which have helped the economy dodge recession.

The US-Mexico relationship is one of the world’s most important bilateral partnerships and while its future is unpredictable, diplomats on both sides of the border credit Sheinbaum with handling a difficult situation well.

“There’s no other government that’s co-operating as much with us in the fight against crime as ... Mexico,” US secretary of state Marco Rubio said while visiting the country last month.

In contrast to some world leaders, Mexico’s president has avoided public spats with Trump over his threats of higher tariffs on trade, preferring private diplomacy.

Advocates hail Sheinbaum as an exemplar, a modern left-wing Latin American leader whose freshness and vitality stand in sharp contrast to some of the region’s other socialists, such as Brazil’s Luiz Inácio Lula da Silva or Argentina’s former president Cristina Fernández de Kirchner.

But critics point to sweeping changes to the judiciary and planned electoral reforms to suggest that behind a technocratic mask, Sheinbaum is an ideologue bent on strengthening what is one of the world’s most powerful presidencies, hastening Mexico’s return to the one-party state that dominated its 20th-century history.

Either way, she faces huge challenges in a country with many regions under the thumb of drug cartels, investors reluctant to commit and an economy that has barely grown in per capita terms for years.

“She’s managed a terribly difficult, adverse situation rather well in her first year, given all the headwinds she has had,” says Jorge Castañeda, a former Mexican foreign minister. “On the other hand, most of the main challenges remain unaddressed.”

Andrés Manuel López Obrador (centre), Claudia Sheinbaum's predecessor as Mexican president, with then defence secretary Luis Sandoval and navy secretary José Rafa