File Photo: The flags of the U.S. and Chinese are displayed together on top of a trishaw in Beijing on Sept. 16, 2018. AP
Here's a rundown of their disputes:
Beijing insists that the balloon, shot down on February 4, 2023, after spending a week flying over the US and Canada, was an errant weather surveillance device. It accused the US of sending its own balloons over China, which Washington denied.
The incident led Secretary of State Antony Blinken to postpone a visit to Beijing that had been billed as a chance to patch up relations.
Beijing has been incensed by US President Joe Biden's defense of self-ruled Taiwan -- especially after he said, first in October 2021, that Washington would defend the island militarily if attacked by China.
In 2022 he rowed back, saying Washington maintained its "One China" policy.
Tensions spiked anew in August 2022 after then-House speaker Nancy Pelosi visited Taiwan.
Beijing carried out unprecedented military exercises around the island in response.
Ukraine and North Korea
Beijing, which claims a policy of neutrality in world affairs, has rejected US calls for it to publicly denounce its ally Moscow over the war in Ukraine.
In February, Blinken accused Beijing of considering arming Russia. Beijing dismissed the claim as "false."
Washington also wants China to rein in North Korea, fearing the reclusive state will soon conduct its seventh nuclear test.
Both Russia and China, North Korea's longtime ally and economic benefactor have vetoed Washington's calls for stronger UN sanctions on Pyongyang.
The question of where the Covid-19 pandemic originated has been the subject of a war of words between Washington and Beijing since the virus first appeared in China in early 2020.
Former US president Donald Trump alleged that the virus was accidentally leaked from a lab in Wuhan, a theory reiterated in February 2023 by FBI head Christopher Wray.
Beijing has strenuously denied the allegation.
Biden, while more measured than Trump, has accused Beijing of hiding important information about Covid's origins.
The world's first (US) and second-largest (China) economies are locked in a fierce battle for control of the semiconductor market.
Taiwan accounts for nearly 50 percent of the world's production of chips used in everything from smartphones and cars to missiles.
Washington has taken steps to limit China's ability to buy and manufacture high-end chips with military applications,
China has taken the US to the World Trade Organization over the restrictions.
Washington in 2021 declared that China's crackdown on the Uyghur minority in the north-western region of Xinjiang amounts to "genocide", a charge rejected by Beijing.
Beijing is accused by rights groups of having detained over a million Uyghurs and other Muslim minorities in camps.
In June 2022, the United States banned most imports from Xinjiang, to punish Beijing for what rights groups say is forced labor in the camps. Beijing denies the allegations.
South China Sea
Washington and Beijing are also at odds over the resource-rich South China Sea.
Beijing claims sovereignty over nearly all of the sea but the Philippines, Vietnam, Malaysia and Brunei say they also own parts of it.
Beijing has ignored an international court ruling which found its claims have no legal basis.
In January 2023, Biden ordered a two-year extension of a program allowing Hong Kong residents in the United States to stay beyond the expiry of their visas.
Biden laid out what he described as the Chinese government's "assault on Hong Kong's autonomy" and its undermining of the territory's democratic institutions.