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The Joint Communiqué on the Establishment of Diplomatic Relations was drawn up on December 15, 1978, by the Carter administration and Deng Xiaoping and stated that public relations will begin between the People's Republic and the United States on January 1, 1979. This document also announced the end of military presence in Taiwan and ended the official recognition of Taiwan as an independent nation. Embassies would be opened in both countries on March 1 of 1979.
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Congress passed a bill that stated the US would continue "cultural and economic" relations with Taiwan but not diplomatic. Even after the Joint Communique, the US still made a point to show it had not turned it's back completely on Taiwan. Of course this did not help build more trust between the States and the People's Republic, but nevertheless having embassies in each country helped the two nations work it out diplomatically.
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As a result of the Taiwan Relations Act, the US continued arms sales to Taiwan between Carter and Reagan's presidency. Reagan was very pro support of Taiwan. This was troublesome to the People's Republic of China. After 8 months of negotiating the two countries came to the conclusion that the US would continue to respect the PRC sovereignty and limit arms sales to Taiwan.
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This trip was an attempt for Reagan to speak on the topic of Taiwanese independence but failed to make up any ground on that topic during this trip. This trip also marked the first serious talks on growing trade between the countries as well as China's nuclear efforts. This was the second visit to China for a US President since Nixon in 1972.
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After the Chinese Military killed hundreds of protestors in Tiananmen Square, President George H. W. Bush agreed with Congress to apply light sanctions on the People's Republic including a ban on arms shipments and halt on talks on nuclear cooperation. Many did not think he had gone far enough but Bush did not want to completely damage diplomacy.
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When the President of Taiwan came to the US to speak about Taiwanese independence, the Peoples Republic took military action and began missile testing in the Taiwan Strait. The US and President Clinton responded by moving US aircraft carriers to Taiwan to prevent further militarya ction. The president then visited China for 9 days in 1998 to repair broken relationships from this Crisis.
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This act normalized trade relations between the two countries and allowed for China to join the World Trade Organization. China opened up its markets to the rest of the world as well removing tariffs. This arguably helped China grow into the economic powerhouse it is today as well as allow farmers and businesses in America to foster from Chinese consumers.
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A Chinese and US aircraft collided in the air and the blame for this collision is disputed to this day. A Chinese airmen was killed and the US crew was detained by the Chinese for 10 days until the US released a letter to the Chinese, that they claim was a letter of regret not apology.
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The US entered into talks with North Korea joined by the People's Republic of China. They were able to get North Korea to agree to turn off Nuclear reactors and close their nuclear program. This showed Chinese and US ability to work together of the disputed Korean peninsula.
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The Obama administration and The People's Republic officials officially met over the course of President Obama's term eight times to discuss economic and military strategy between the two nations.
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President Obama officially recognizes disputed Tibet region as a part of the People's Republic of China.
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Trump directed tariffs to be placed on steel, aluminum, and other Chinese imports. China responded by placing tariffs on soy and other American exports to China.