They are the leaders of the world's two biggest economic powers, and they have sharply different visions and personalities.
As United States president Donald Trump sat down for dinner with Chinese counterpart Xi Jinping, he told the waiting media it was the beginning of a special relationship.
"It's an honour to have you in the United States. We've had a long discussion already. And, so far, I have gotten nothing, absolutely nothing. But we have developed a friendship, I can see that. And I think, long-term, we're going to have a very, very great relationship, and I look very much forward to it."
But just a few hours earlier aboard his Air Force One presidential plane, Mr Trump was more than a little less cordial in tone amid the static.
"We have been treated unfairly and have made terrible deals, trade deals, with China for many, many years. So that's one of the things we'll be talking about. The other thing, of course, is going to be North Korea. And, somehow, they will mix. They really do mix."
It is being called the most consequential meeting of Donald Trump's presidency so far.
Just a few kilometres away from his Mar-a-Lago resort in the state of Florida, where the talks are being held, Chinese imports continue to be unloaded from container ships.
But the amount of US goods going the other way is not anywhere near as much, prompting Mr Trump to threaten to introduce tariffs - which could spark a trade war.
The mayor of local Miami-Dade County, Carlos Gimenez, says that needs to be avoided.
"The President would like to see more of a balance in the exports and imports, but I don't think we're going to get into a trading war with China. Again, it would not be good for the United States, and it wouldn't be good for China either."
A director of the Washington-based research centre the Brookings Institution, Thomas Wright, says some members of the Trump administration have conflicting views about China.
He points, in particular, to Donald Trump's chief strategist, Steve Bannon, and secretary of state Rex Tillerson.
"Steve Bannon, in particular, believes that China's only succeeded economically at the expense of the United States, and President Trump has sort of said very similar things. And that view, and the idea that the US only really succeeds if China fails economically, is a pretty fringe view and, I think, would have grave consequences for the global economy and for the US economy. So that's a risk. But Secretary Tillerson and some others are sort of making more of a case for engagement and a more traditional and balanced approach."
It is an approach Mr Tillerson once again adopted ahead of President Xi's arrival.
"Today will be a time to exchange candid views on the nature of the US-China relationship, and we look forward to additional discussions in the future on topics of mutual importance. As President Trump has said, the chief goal of our trade policies is the prosperity of the American worker. To that end, we will pursue economic engagement with China that prioritises the economic wellbeing of the American people."
As for foreign policy, another pressing issue shared between China and the United States is the instability coming out of North Korea.
Mr Trump says China should be doing more to discourage Kim Jong-un's nuclear program and has even threatened to deal with North Korea alone if he has to.
The Brookings Institution's Johnathan Pollack warns that would not be a wise move.
"We're going to do a lot better at it if we are doing this in conjunction with China and with the Republic of Korea than if we're trying to do it separately."
But Zhao Tong, from Beijing's Carnegie-Tsinghua Centre, says he believes, while President Xi has little trust in Kim Jong-un, he has even less for President Trump.
"China believes that the US is using North Korea as an excuse to deploy aggressive, strategic military assets close to China and is using those military assets to contain China militarily."
The official talks are set to begin later tonight.
