Claudia Sheinbaum's election win changes Mexico's 'macho' society forever

For the past three weeks or so I've travelled the entire length of Mexico, from its border in the south with Guatemala to its northern state of Chihuahua that borders the US.

In cities, towns, and villages, ubiquitous billboards for the various political parties and candidates dominated the skyline.

Claudia Sheinbaum's face was as common a signpost as the fast-food restaurants - which is something of a national obsession here.

What was interesting though, was that in some of the poorest areas we visited, on the porches and in the windows of some of the most modest houses, and in some cases, even slums, Sheinbaum's campaign posters were proudly displayed.

Her predecessor and mentor, President Andres Manuel Lopez Obrador, universally known as AMLO, has handed his prodigy a game-changing electoral ticket, with his social reforms that include universal pensions for the poorest.

It's hugely popular and has basically set up Sheinbaum and the Morena party for political dominance.

Of course, the fact that the two frontrunners for this election were women guaranteed this was to be a historic moment for Mexico.

The president-elect, who takes over in October, greeted the large crowds gathered in Mexico City's famous Zocalo Square, acknowledging immediately that while she has so much political work to do, the moment itself is historic and has changed the usual 'macho' politics and society forever.

Across the country, electoral lawyers like Susana Mercado pored over the results as they were coming in. This wasn't just a presidential election, it's also about control of congress, and with it, all of government.

And for the faithful, Ms Mercado included, it's a new beginning for Mexico.

This moment, she says, means everything to her.

"Having the first female president in North America is very symbolic in a country such as Mexico because machismo here is something that is very hard to work with, and women in spaces of power really have to struggle to get there," says Ms Mercado.

"So I am a big fan of the president right now, and we can be very happy because people went out and voted for a woman in Mexico - it's blowing my mind."

Even in the conservative northern state of Chihuahua, where the Morena party is less popular than in metropolitan areas, I met women who said they were pleased that a woman had won, even if they fundamentally disagree with the new president's politics.

One woman who stopped to chat, but didn't want to appear on camera, told me it was a significant day.

"Look, it's good a woman won, it's about time," she told me, while overseeing a group of schoolchildren on a day out.

"I don't even dislike Claudia, but I hate her party, and her socialist boss," she said.

Many here believe AMLO, who under the constitution can only be president for one term, will still be pulling the strings.

Candidates assassinated

In what has been the deadliest electoral cycle in Mexico's history, with over 30 candidates assassinated before the vote, it's hardly surprising that security, and how to control the incredible power and reach of Mexico's cartels, was the top political issue for most voters.

Sheinbaum has promised to do something about the problem but hasn't indicated how she plans to do it.

Her other big issue, as always for Mexico's leaders, is overseeing relations with the United States - this country's biggest trading partner.

Migrants from around the world passing through Mexico to the US isn't necessarily a political issue here because migrants usually just continue north.

But Joe Biden and Donald Trump will spar over the problem at the border in coming months, ahead of their own presidential election.

Steering a course with whoever wins the US election will be a major test for Claudia Sheinbaum.