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Chinese-U.S. ties are at their lowest point in decades.

The most vital and sensitive issue for Beijing?

Not trade, not Huawei… but Taiwan.

In the middle of September, China sent jets close to the island for two days of military drills - prompting a scramble of Taiwan’s air force.

Let’s look at why tension is rising around the small island and why it involves Washington.

China claims democratically-run Taiwan as its own territory, to be taken by force if needed.

The island has lived with that threat since 1949 when nationalist forces defeated in the Chinese civil war fled there.

The U.S. has stepped up support for Taiwan lately, sending top officials for two visits in as many months.

[U.S. health chief Alex Azar, saying:] "The United States knows that we will always have a friend in Taiwan."

That plus major new arms sales.

To China, the U.S. is effectively backing Taiwanese independence.

Why is the island so vital?

Two reasons: firstly, geography.

It lies in a key location on the edge of the Pacific, between the disputed South China Sea and Japan.

Secondly, it’s a tech powerhouse, home to the world's biggest contract chipmaker, Taiwan Semiconductor Manufacturing.

The U.S. sees Chinese tech firms as a security risk and has moved to cut off its access to advanced chips, including those from Taiwan.

Taiwan and China have no official dialogue mechanism, meaning any small spark could quickly escalate.

Taiwan's military is well-trained and well-armed but dwarfed by China's People's Liberation Army, which is in the throes of an impressive modernisation programme.

Taiwan's president has made upgrading the military a priority, stressing, quote, "asymmetric warfare."

But China could easily overwhelm Taiwan with missiles, air attacks, cyberattacks, or a naval blockade.

China’s foreign ministry spokesman: "Taiwan authorities are spending their taxpayers' money on defense, but no matter how much it spends on defense Taiwan is still a tiny place. Confronting the mainland is like an ant trying to shake a tree."

A conflict over Taiwan may suck in the United States and its Asian allies, though it is an open question whether or not Washington would come to Taipei's aid.