(CNN) President Donald Trump will arrive Thursday at the G20 summit in Osaka, Japan -- his third time attending the yearly gathering as President and, in some ways, the most consequential.

Unlike Trump's recent state visits to Tokyo and London, this stop is not about pageantry -- or really even about him. Instead, it's a gathering of leaders from the world's largest economies meant to discuss pressing economic and geopolitical issues. Though the leaders all meet together several times, the real action takes place on the sidelines when one-on-one talks between countries can produce major announcements.

Trump has clashed with many of the other G20 leaders on trade and security matters. With some top American allies, he seems to lack chemistry. Other, more adversarial leaders have had better luck.

Here's a look at who Trump will encounter this week, and the state of his relationships:

Chinese President Xi Jinping

Trump's Saturday meeting with his Chinese counterpart -- meant as a face-to-face dialogue on trade -- will be the centerpiece of his stop in Osaka. Depending on its outcome, it could send ripples through the global economy. Trump has frequently said he enjoys a "great relationship" with Xi, with whom he toured the Forbidden City in Beijing in 2017 and later hosted at Mar-a-Lago.

But the limits of personal friendship were tested this spring when China backed away from verbal commitments in a nascent trade agreement. They will be tested again as the two leaders work to get trade negotiations back on track -- and tamp down a trade war that has injected anxiety into the global economy.

Trump is "quite comfortable with any outcome of those talks," one US official said this week. "It's really just an opportunity for the President to maintain his engagement."

Russian President Vladimir Putin

Perhaps no other world leader has captured Trump's imagination like Putin, the enigmatic former spy who admitted during a news conference last year that he had wanted Trump to win in 2016. The means by which Putin sought to make that happen -- cyber interference, according to US intelligence assessments -- are the basis for the dark undercurrent of "witch hunt" obsession that colors Trump's presidency.

Trump has said the investigations into Russian election interference have hurt relations between the two countries, which he wants to improve. That includes through a new nuclear arms treaty that would include China. But election meddling aside, the two countries are far apart on issues like Ukraine and Syria.

US officials this week stressed that Trump's meeting with Putin at the G20 was not a formal summit but rather a "normal event" without a "formal agenda."

Japanese Prime Minister Shinzo Abe

The host of this year's G20, Abe has worked harder to cultivate Trump than perhaps any of his global counterparts. There are the rounds of golf, the custom-made ball caps, the across-the-globe flight to attend Melania Trump's birthday party this spring. A month later, Trump was standing in a sumo wrestling ring awarding a human-sized trophy, all orchestrated by the Prime Minister.

It's part of an effort to maintain close US-Japan ties, particularly as Trump pursues diplomacy with North Korea and wages trade war with China. Whether Abe's efforts are paying off remain to be seen: During his Tokyo visit, Trump publicly broke with Abe on the seriousness of North Korea's recent short-range missile tests.

French President Emmanuel Macron

They were once the closest of friends: After an invite to Paris for a Bastille Day military parade, Trump reciprocated by hosting Macron and his wife for his first (and currently only) state dinner in Washington. But since then their bond has frayed, and it almost broke in November when Trump insulted Macron over Twitter during another visit to Paris.

Now the two men appear to be at least on working terms. They met earlier this month in Normandy during a D-Day commemoration ceremony and are expected to confer on Iran during this week's G20.

German Chancellor Angela Merkel

Unlike some of her counterparts, Merkel has never attempted lavish displays of flattery to woo Trump. Instead, she's remained a businesslike and dutiful counterpoint to Trump's brash pronouncements, particularly when it comes to the European Union.

Once seen as the leader of the bloc, Merkel has since been politically humbled, and she announced last year that her fifth term as chancellor will be her last. She's taken her share of Trump's arrows, particularly when it comes to trade. Her close relationship with President Barack Obama hasn't helped her with Trump. But in her unwillingness to adopt the same obsequiousness as her peers, she seems to have gained a modicum of his respect.

British Prime Minister Theresa May

After two and a half years of highs and lows -- and they were mostly lows, including an insulting interview Trump gave The Sun newspaper last year and repeated questioning of her plans for Brexit -- Trump offered only praise for May during his visit to London earlier this month.

Perhaps that was because May is stepping aside, with her replacement to be chosen in the coming weeks. Trump seemed to admit she'd been dealt an impossible hand and had played it the best she could. Still, the differences in temperament between the two "special relationship" leaders were always apparent. The front-runner to succeed May, Boris Johnson, is far more Trump's style.

Saudi Crown Prince Mohammed bin Salman

Once viewed as a young reformer, Prince Mohammed (known universally by his initials, MBS) has since gained a reputation as another Middle East strongman willing to use authoritarian measures to stamp out dissent -- including, in his case, the journalist Jamal Khashoggi, who was killed last year.

That episode hasn't dampened Trump's view of the kingdom, however, and just this week he brushed aside a UN report calling for the FBI to investigate the killing. Instead, he says he'll continue doing business with MBS. They spoke about Iran by phone last week.

In Osaka, the men will discuss "the escalation in the region as a result of Iran's provocative acts" and focus on "ways to address regional stability," an administration official said.

Turkish President Recep Tayyip Erdoğan

Erdogan reliably caused headaches for American presidents before Trump and that pattern hasn't abated. The current dispute centers on Turkey's purchase of a Russian missile-defense system, which would trigger automatic sanctions from the US. The Pentagon has also threatened to withhold F-35 fighter jets Turkey was planning to purchase.

Erdogan hopes to change Trump's mind during in-person talks at the G20. And there's reason to believe he could: During a December phone call, Erdogan argued against the presence of US troops in Syria. A short time later, Trump announced he was withdrawing.

Canadian Prime Minister Justin Trudeau

For the first half of Trump's term, he and Justin Trudeau were locked in a trade battle that largely crowded out other areas of the US-Canada relationship. Things got ugly.

But US and Canadian officials say the men's relationship has rebounded since Trump called Trudeau "very dishonest and weak" almost exactly a year ago. Now they hope to partner on issues such as China, which has detained two Canadian citizens. Still, their ideological differences are stark. And like Merkel, Trudeau's close relationship with Obama doesn't help him in Trump's eyes.

Mexican President Andrés Manuel López Obrador

López Obrador isn't actually attending the G20 -- he announced earlier this month he did not want to get drawn into US-China trade disputes, which could dominate the summit. He will send a representative instead. Still, Trump's relationship with Mexico is one of his most tumultuous. He's gone from lambasting the country for its immigration enforcement measures -- evening threatening tariffs -- to praising it.

A NAFTA replacement package has eased trade tensions for now. But the cross-border ties are likely to remain bumpy for the foreseeable future.

The rest of the group

Other leaders gathering at the summit are those from Argentina, Australia, Brazil, the European Union, India, Indonesia, Italy, South Africa and South Korea.

Trump has fostered amiable ties with some of the other G20 leaders -- including Brazilian President Jair Bolsonaro, who has adopted some of Trump's populist themes, and Argentine President Mauricio Macri, who he knew as a business developer. He won't meet them in Japan, however.

He is due for talks with the new Australian prime minister, Scott Morrison, whom he congratulated for a "GREAT WIN!" on Twitter last month.

And he'll meet with Indian Prime Minister Narendra Modi, who also won his election in May.