Trump meets world: With his past comments, this could get awkward

Trump's first day: What's on the agenda?
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(CNN)It's time to get to work for US President Donald Trump, and that involves meeting his counterparts across the globe.

He'll start this week with British Prime Minister Theresa May, who's already expressed consternation over his past inflammatory comments.
Some of those could make for some interesting encounters with world leaders. Here are a few where it would be fascinating to be a fly on the wall.

NATO

    Donald Trump calls NATO 'obsolete' during GOP town hall
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    Donald Trump calls NATO 'obsolete' during GOP town hall 02:05
    What he said: "NATO had problems. Number one it was obsolete, because it was, you know, designed many, many years ago. Number two -- the countries aren't paying what they're supposed to pay."
    -- Donald Trump, in an interview with The Times of London and BILD published on January 16, 2017
    It might make things awkward with: The leaders of NATO member states and NATO Secretary General Jens Stoltenberg
    Context: It's not the first time Trump has called NATO obsolete, and the statement is in line with Trump's campaign promise to rethink the US role in the world -- specifically whether it is spending too much money abroad.
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    When he'll see them: British Prime Minister Theresa May is traveling to Washington Friday to become the first foreign leader to meet with Trump as US President.
    May spoke with Stoltenberg Sunday night, telling him that she would reiterate the alliance's importance to Trump, according to a statement from 10 Downing Street.
    NATO announced last summer it would hold its annual summit at its new Brussels headquarters sometime in 2017, though the specific date has not been announced. Trump's likely to meet Stoltenberg and other NATO leaders then, if not before.

    United Kingdom

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    Trump's uncensored lewd comments about women from 2005 02:45
    What he said: "When you're a star, they let you do it. You can do anything ... Grab 'em by the pussy. You can do anything."
    -- Donald Trump, caught on a hot mic in 2005 speaking to Billy Bush, then-host of "Access Hollywood"
    It might make things awkward with: British Prime Minister May when they meet Friday.
    Context: The footage of Trump's comments describing sexual assault surfaced in October. With people on both the left and right slamming him, it nearly brought down his campaign.
    Trump quickly apologized, saying he is not a "perfect person." He also took a stab at former Bill Clinton, alleging the former President "has said far worse to me on the golf course."
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    Will it come up? Unlikely.
    May said in an interview with the BBC she and Trump will be talking about NATO, trade and the Syrian conflict, not Trump's past comments.
    But May, who's already called those comments "unacceptable," said she would call out the new President if he were to say something out of line.
    "Whenever I find there is something unacceptable, I won't be afraid to say that to Donald Trump," she said. "I think the biggest statement that will be made about the role of women is that fact that I will be there as a female prime minister, Prime Minister of the United Kingdom."

    Mexico

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    Donald Trump on Mexico: Then and Now 01:02
    What he said: "When Mexico sends its people, they're not sending their best. ... They're sending people that have lots of problems, and they're bringing those problems with us. They're bringing drugs. They're bringing crime. They're rapists. And some, I assume, are good people."
    -- Donald Trump, announcing his candidacy on June 15, 2015.
    It might make things awkward with: Mexican President Enrique Peña Nieto
    When they'll meet: Probably soon -- a presidential memo released shortly after his election said that Trump would begin reforming NAFTA on Day 1.
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    President Trump said Sunday he will start renegotiating the North American Free Trade Agreement (NAFTA) -- one of his big campaign promises -- when he meets with his Mexican and Canadian counterparts.
    It won't be the first time Trump meets Peña Nieto in person -- the two met privately and held a joint news conference in August.
    Trump struck a cordial, diplomatic tone while addressing the press after the meeting, but used much more hostile rhetoric when discussing Mexico in a press conference hours later.

    China

    Trump questions 'one China' policy
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    Trump questions 'one China' policy 00:55
    What he said: "I fully understand the 'One China' policy, but I don't know why we have to be bound by a 'One China' policy unless we make a deal with China having to do with other things, including trade."
    -- December 11, 2016, in an interview with Chris Wallace on "Fox News Sunday"
    It might make things awkward with: Chinese President Xi Jinping
    Context: The comments came after the then President-elect took a congratulatory phone call from Taiwan's President Tsai Ing-wen in violation of longstanding diplomatic protocols surrounding the "One China" policy.
    China views Taiwan as a renegade province and, since 1979, the US has acknowledged Beijing's claim that Taiwan is part of China, with US-China relations governed by a set of protocols known as the "One China" policy.
    This means there are no formal diplomatic relations between the United States and Taiwan -- so Trump's decision to take Taiwanese President Tsai Ing-wen's call could risk a major upset.
    For decades, the policy has been the linchpin of the Washington-Beijing relationship, and now Trump is saying it's negotiable.
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    President Trump has promised to rethink the US' role in the world, taking a cost-benefit analysis to its relationships, especially in East Asia. The "America First" theme was on full display during his inaugural address, much to the chagrin of foreign diplomat
    When they'll see each other: Although Trump or Xi could travel to their respective countries for bilateral meetings, they'll likely both be at the G20 summit in July.