Here is a recap of why relations between the US, China and Taiwan are so delicate:

- Bitter history -

The deep rift between Beijing and Taiwan dates back to China's civil war, which erupted in 1927 and pitted forces aligned with the Communist Party of China against the Nationalist Kuomintang (KMT) army.

Eventually defeated by Mao Zedong's communists, KMT chief Chiang Kai-shek fled to Taiwan, which was still under his control.

From there, Chiang continued to claim the entirety of China -- just as the mainland claimed Taiwan as part of its territory to be re-taken one day.

Taiwan's official name remains the Republic of China, while the mainland is the People's Republic of China.

For years both sides still formally claimed to represent all of China, although that landscape has changed in recent decades.

Since the late 1990s, Taiwan has transformed from an autocracy into a vibrant democracy and a distinct Taiwanese identity has emerged.

The current ruling party, led by President Tsai Ing-wen, regards Taiwan as a sovereign nation, not part of China.

- Strategic ambiguity -

Washington cut formal diplomatic relations with Taiwan in 1979, switching recognition to Beijing as the sole representative of China, with the mainland becoming a major trading partner.

But at the same time the United States maintained a decisive, if at times delicate, role in supporting Taiwan.

Under a law passed by Congress, the United States is required to sell Taiwan military supplies to ensure its self-defence against Beijing's vastly larger armed forces.

But it has kept a "strategic ambiguity" on whether it would actually intervene militarily, a policy designed both to ward off a Chinese invasion and discourage Taiwan from ever formally declaring independence.

There is now growing bipartisan discussion in Washington over whether a switch to "strategic clarity" is preferable given Beijing's increasingly bellicose approach to cross-strait relations.

Russia's war on Ukraine has heightened fears that China might one day follow through on threats to annex its smaller neighbour.

When Biden was asked in Tokyo on Monday whether the United States would get involved militarily to defend Taiwan, he replied in the affirmative, adding: "That's the commitment we made."

But the White House and Pentagon moved quickly afterwards to state that US policy "has not changed" on Taiwan.

Biden has made similar remarks before in lower-profile settings, which were also later clarified in the same way.

-'One China' policy -

US policy on Taiwan has always hinged on diplomatic nuance.

In what is termed the "One China policy", Washington recognises Beijing, but only acknowledges the Chinese position that Taiwan is part of China.

It leaves it to the two sides to work out a solution, while opposing any use of force to change the status quo.

In practice, Taiwan enjoys many of the trappings of a full diplomatic relationship with the United States.

While there is no US embassy in Taipei, Washington runs a centre called the American Institute in Taiwan.

In the United States, the island's diplomats enjoy the status of other nations' personnel.

Only 14 nations, all in the developing world, and the Vatican still recognise Taiwan.

Beijing has tried hard to stop any international recognition for the island.

It baulks at any use of the word Taiwan, such as when Lithuania allowed Taipei to open a de facto embassy under its own name last year, lest it might lend the island a sense of legitimacy on the global stage.

The United States and a growing number of countries have pushed for Taiwan to be included in UN bodies such as the World Health Organization (WHO).

Taipei accused Beijing of "bullying" on Monday after the WHO annual assembly refused to discuss admitting Taiwan as an observer, despite support from several countries, after pressure from China.