"America," Donald Trump said today during his inauguration, is going to “start winning again.”

From now on, it’s going to be “America first” — and that mentality, he said, will surely lead to “great prosperity and strength.”   

About that, opinions run the gamut. We checked in with some of our journalists and other correspondents from across the globe — to get a sense of what people are thinking and feeling about the new US president — from Russia, where there's a big market for Trump merchandise, to Mexico, where even schoolchildren watched the inauguration live on TV.

Read on, or listen to the audio stories, below:

Recently, Trump hasn't seemed too close to Mexico. He wants to build a bigger wall at the border, he's made disparaging comments about Mexican immigrants and he's tried to convince American automakers to shift production north. Not to mention, he made it clear in his inaugural address that his foreign policy is all about putting America's interests ahead of everyone else's. 

In general, Mexicans are worried about what all of this means for them, says The World's Monica Campbell who's based in Mexico City. "Everyone I've talked to is just in a real wait-and-see mode."

It doesn't help that the country is in the midst of a crushing economic crisis — tied to a drop in gas prices. A Trump presidency, Campbell says, could make it worse. “Throughout Trump's campaign, every time he bashed Mexico, the peso lost value." In fact, last week it hit a record low of 22.04 pesos per dollar, and it hasn't improved much — today it's 21.54 pesos per dollar.

Despite Trump's impact on their economy, Mexicans have a grasp on the bigger picture — they know that the branches of government check and balance each other, that you have to "go through Congress to do certain things. You can't just slap tariffs automatically," says Campbell. "And they're hoping that over time [Trump will] see that Mexico and the US are partners.”

After last night's extradition of drug king, Joaquín "El Chapo" Guzmán, to New York from Ciudad Juarez, Campbell says there's at least a chance of that. "This could be interpreted by Trump as a sign that Mexico is willing to work with the United States in terms of tackling cartel violence in Mexico." Many of today's headlines in Mexico were along the lines of "Trump in, El Chapo out." 

So, Mexicans are paying close attention to Trump, she says. For example, during the inauguration, “while Trump was speaking, I caught on Twitter a couple of pictures of classrooms in Mexico watching the speech." 

One issue that's on many people's minds, here, is the future of DACA (Deferred Action for Childhood Arrivals), which protects people who came to the US as children, without the proper papers. It began under Obama.  

Hundreds of thousands of young people have signed up for DACA, but the president can nix the act — simply with a signature, she says. "If he does, that will show that this is going to be really hard-line administration when it comes to immigrants and immigration policy." 

Plenty of Russians are partying tonight to celebrate Trump — and what they see as the start of a new, friendlier era with the United States.

That's according to Moscow-based journalist Charles Maynes.

“Pro-Kremlin youth activists are throwing an all-night party at the former Soviet post office downtown here,” he says. “The featured theme of the event is 'the new world order.'”

It comes with its own art: a triptych — several paintings of a slightly touched-up Trump, Russian President Vladimir Putin and Marine Le Pen from France — “advertising this idea that somehow with Trump’s ascension to the presidency, you’re going to see a completely different world order.”

One of the reasons the Russians are so elated, right now, he says, is because the media, here, has been stoking fears of an impending military confrontation with the United States. “By contrast, Trump is shown as the candidate for peace,” he says.  

Not to mention, there’s money to be made, as well — Trump sells: “We have commemorative coins issued in the Urals — this is a series called, ‘In Trump We Trust,’” says Maynes. 

Sugar cubes, issued in Tula, are about “sweetening” relations. There are also Trump nesting dolls, Trump burgers, Trump charcoal, out of Siberia, even an army fashion line that's offering a 10 percent discount to US embassy officials and US citizens. 

"Finally, also we have Trump 'bling' — probably the most Trumpian of all [the merchandise]," he says, referring to a commemorative, gold-encrusted Donald Trump smartphone case (specifically for the iPhone 7), which goes for $3,000. 

These ventures are kind of opportunistic, Maynes says, but he thinks the enthusiasm he's seeing is genuine.

Not so much with the country's intellectuals, or experts and analysts, though. They're more skeptical, reflecting on how things tend to go back and forth. For a while. "You have these ingrained interests that will test both leaders, and at some point … this is all going to fall apart, and we’re going to go back to basically an adversarial relationship,” Maynes says.  

Lately, Turkish President Recep Tayyip Erdogan has had a “soothing tone” towards the US, says PRI's Richard Hall, who is based in Beirut and reports on the Middle East. “[Erdogan] says he hopes that Trump can mark a departure from the policies of Obama.” 

And other leaders in the region are optimistic about the Trump administration, like in Israel. Leaders there are looking forward to a closer relationship with the US, he says.

But in Syria, people are more nonchalant, he says. For starters, the Syrian government viewed Obama as “an aggressive US leader that was trying very hard to change the regime."

Obama didn't fare much better among Syrian activists, either. That's because when Obama took office, Hall says, he made a point of taking a strong stand against Syrian President Bashar al-Assad. 

He took a hard line against chemical weapons, threatening military action if the Syrian government resorted to that — and yet, when Assad did, Obama didn’t come through. 

As a result, Syrian activists are deeply disappointed in Obama. “After a while, they didn’t really expect much from Obama ... so now there is a sense that Trump can’t be really much worse,” Hall says. “Obama to them promised all these things, and he didn’t deliver. Trump isn’t promising anything, and he won’t deliver for them either.”

While threading his way through the crowds at Donald Trump’s inauguration on Capitol Hill today, Rahul Joglekar couldn’t help but think of cricket. 

For Joglekar, a British Indian reporter for the BBC Asian Network, who is in Washington, DC, this week, the atmosphere here sort of channels the fervor surrounding a cricket match between India and Pakistan “where even though you know who the man of the match is, you have people from both sides who are making their voices heard and want to be counted.”

Also, as he's been following Trump, Joglekar has found similarities between President Trump and Indian Prime Minister Narendra Modi. 

“The first parallel is that no one would have expected Narendra Modi to win, firstly, backing from his own party, and, secondly, a landslide victory in the Indian elections,” he says. “And that’s exactly what happened with Donald Trump.”

On top of that, according to Joglekar, the two leaders have similar messages: “They both sort of talk, almost as if there is a promised land,” says Joglekar. “Narendra Modi didn’t say, ‘Let’s make America great again,’ but that could very well have been his election slogan, as well, talking about the India that was, and the culture and the heritage that India has.”

PRI's Richard Hall, Carol Hills, Lidia Jean Kott and Christopher Woolf contributed to this report. 

From PRI's The World ©2016 PRI