Short answers, pulled from the story.
The United States formally established diplomatic relations with the People's Republic of China on the 1st of January 1979, transferring recognition from Taipei to Beijing via the Joint Communiqué on the Establishment of Diplomatic Relations. Embassies opened in each other's capitals on the 1st of March 1979.
Ping-pong diplomacy refers to the April 1971 visit of American table tennis players, including Glenn Cowan, to China following a friendly encounter with Chinese player Zhuang Zedong in Japan. Chairman Mao personally approved the invitation, making the athletes the first Americans to officially visit China since the communist takeover. The episode helped pave the way for President Nixon's 1972 visit to Beijing.
The Shanghai Communiqué, issued at the conclusion of Nixon's visit from 21 to the 28th of February 1972, had the United States acknowledge the Chinese position that all Chinese on both sides of the Taiwan Strait maintain there is only one China and that Taiwan is part of China. The statement allowed the US and the PRC to temporarily set aside the Taiwan issue and open trade and communication.
Chinese leadership was alarmed by the UN offensive crossing the 38th parallel in September 1950, which threatened to place an American-aligned state directly on China's border. In August 1950, Mao Zedong told the Politburo that a US victory would leave America in a position to threaten China. Premier Zhou Enlai warned the US publicly that China would intervene on national security grounds; the warning was dismissed by President Truman. Chinese forces crossed into North Korea on the 19th of October 1950.
The Tiananmen Square crackdown led the United States to suspend high-level official exchanges with China, freeze weapons exports, and impose economic sanctions. The US Trade and Development Agency suspended all new activities in China from June 1989 until January 2001. US-China military ties were terminated in 1989 and, as of 2024, have never been restored.
As of 2025, the United States and China are the world's largest and second-largest economies by nominal GDP. Collectively they account for 44.2% of global nominal GDP.