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. This transfer of recognition moved from Taipei to Beijing and was followed by the opening of embassies in each other's capitals on the 3rd of March 1979.
Chinese public opinion turned hostile toward the United States following events that included military exercises conducted by the People's Liberation Army in the Taiwan Strait in 1996. These actions triggered the Third Taiwan Strait Crisis, prompting the United States to dispatch two aircraft carrier battle groups to the region.
American ping-pong player Glenn Cowan met Zhuang Zedong in Japan in April 1971, an encounter that Chairman Mao personally approved as a friendly exchange known as ping-pong diplomacy. Henry Kissinger subsequently traveled secretly to Beijing to negotiate with Premier Zhou Enlai, leading to President Nixon's visit to Beijing, Hangzhou, and Shanghai between 21 and the 28th of February 1972.
Donald Trump launched a trade war with China in 2018 when Chinese authorities enforced punitive tariffs on 128 categories of American goods starting the 1st of April 2018. By late September 2018, the Trump administration placed 25% tax increases on $250 billion worth of Chinese goods.
As of 2025, the United States and China remain the world's largest and second-largest economies by nominal GDP. Together they account for 44.2% of global nominal output while maintaining persistent disputes over economic policies and territorial claims in the South China Sea.