These are the key takeaways from Trump-Xi meetings in China

[0:00] President Trump traveled to Beijing for a summit with Chinese President Xi Jinping [0:05] during a crucial moment of his second term in the White House. [0:09] The historic gathering comes as the Iran War continues to impact global oil supplies [0:15] and the transit of goods through the Strait of Hormuz. [0:18] But top of mind for President Xi, Taiwan. [0:22] I'm Olivia Gazis for CBS News, [0:24] and these are the top five highlights from President Trump's trip to China. [0:29] President Trump arrived in Beijing to a welcome ceremony with pomp and pageantry. [0:35] On Thursday, before a closed-door session, President Trump praised President Xi [0:46] and touted the tech leaders who accompanied him to China [0:49] to encourage new partnerships between the two world superpowers. [0:53] Just want to say on behalf of all of the great delegation that we have, [0:58] we have the greatest businessmen, the biggest, and I guess the best in the world. [1:02] We have amazing people, and they're all with me. [1:05] Every single one of them, we asked the top 30 in the world, [1:09] every single one of them said yes. [1:12] And I didn't want the second or the third in the company. [1:15] I wanted only the top. [1:16] And they're here today to pay respects to you and to China. [1:20] And they look forward to trade and doing business, [1:23] and it's going to be totally reciprocal on our behalf. [1:27] Then a high-stakes closed-door meeting that lasted over two hours. [1:31] According to Chinese state media, Xi issued a stern warning about Taiwan, [1:37] saying potential clashes and even conflicts could happen if the issue isn't handled properly. [1:44] The White House called the meeting good. [1:47] Here's more from CBS News' Weijia Jiang and Tony DeCoppo. [1:51] We should be partners, not rivals. [1:54] There, they stress the importance of cooperation. [1:57] It's an honor to be with you. It's an honor to be your friend. [2:01] And the relationship between China and the USA is going to be better than ever before. [2:06] The White House says both presidents agreed on the need for China to buy more U.S. agricultural products. [2:13] Overnight, China approved export licenses for more than 400 American beef processing plants, [2:19] according to customs data. [2:21] For Xi, Taiwan is top of mind. China wants reunification. [2:28] And for the U.S. to stop selling arms to the self-governing island. [2:32] Chinese state media says Xi raised the issue today, [2:36] warning differences could bring the U.S. and China into, quote, [2:40] conflict. But Trump declined to say whether it was discussed. [2:44] Mr. President, did you talk about Taiwan? [2:46] And the White House did not mention Taiwan in the formal summary of their meeting. [2:52] It did include the war in Iran, saying Xi agreed with Trump that the Strait of Hormuz [2:57] must remain open and that Iran can never have a nuclear weapon. [3:02] Why does China care so much about Taiwan? They consider it to be part of mainland China. [3:08] It splintered off in 1949 after the Chinese Civil War, [3:13] and Beijing regards it as essentially a renegade province, [3:17] not unlike an American state that's trying to secede. [3:20] And they want America to stop selling arms to this, [3:24] in essence, state that's trying to secede in their view. [3:27] And that's why it is such a core issue for them. 1949 looms large. [3:32] By 2049, the 100-year anniversary of the modern China, [3:37] they hope that there will be reunification. [3:40] What the people here hope, though, is very different, Errol. [3:43] We spent some time today at a market, at the mall, in a subway station, [3:47] talking to anyone who would talk to us about how they feel being Taiwanese [3:53] so close to the Chinese mainland. And the general perspective is that [3:56] there's nothing against China per se, but they don't want to be communist in any country. [4:02] They have grown attached to their independence, [4:05] to their freedoms, to the democracy that they have here. And that's really where they draw the line. [4:11] They don't care what name you put on it. If you call them a country or a nation [4:16] or an independent province, they're comfortable with the status quo, [4:20] but they don't want to be gobbled up by their bigger neighbor. [4:23] Trump and Xi later visited the Temple of Heaven before members of the Chinese [4:28] and American delegations attended a state banquet on Thursday. [4:32] There, Xi and Trump toasted the relationship between the U.S. and China. [4:37] We had extremely positive and productive conversations and meetings today. [4:41] On Friday, Trump's second full day in Beijing, he met with Xi Jinping for tea [4:47] and a walk around a centuries-old garden where the two, according to President Trump, [4:52] discussed the Strait of Hormuz and potential trade deals. Here's more from Weijia Jiang. [4:58] It was the final event for President Trump's two-day visit here where Iran, [5:03] Taiwan and trade dominated the conversations. Trump said it was a successful meeting and Xi [5:08] called it a historic summit as Beijing gave Trump a lavish send-off. [5:13] China rolled out the red carpet one last time for President Trump. [5:19] before he waved goodbye to his hosts and boarded Air Force One back to the U.S. [5:27] Trump and Chinese President Xi Jinping capped off their final day together, [5:32] walking around the historic Zhongnanghi Garden. [5:35] Nice, nice place. [5:36] But after a two-day display of diplomacy, [5:40] it's still to be seen how much progress they made to resolve tension over several topics. [5:45] We've settled a lot of different problems that other people wouldn't have been able to settle. [5:49] Xi told Trump Taiwan was the most important issue in the U.S.-China relationship and warned [5:55] mismanagement could have consequences. [5:58] He feels very strongly. I made no commitment either. [6:01] Trump said China agreed to buy American oil, 200 Boeing jets and soybeans. [6:07] The farmers are going to be very happy. They're going to be buying billions of dollars of soybeans. [6:13] President Trump has invited President Xi for a reciprocal visit in the U.S. in September. [6:18] He's headed back to America, having apparently shored up his relationship with Xi, [6:23] but his major flashpoints remain. Iran, Taiwan, the fate of China's political prisoners, [6:30] and the details of major trade agreements all appear unresolved for now. Olivia Gazis, CBS News, Washington.