Taiwan says China ran illegal surveillance on the president's family on American soil, a bad sign for Taiwanese living abroad and another low point in China-Taiwan relations.

• The FBI arrested a Chinese woman at Los Angeles International Airport, accused of spying for Beijing.
• She is alleged to have watched Lai Ting-yu, the son of Taiwanese President Lai Ching-te.
• Taiwan's foreign ministry condemned the operation as cross-border repression and asked other countries to speak out and push back together.
• Taipei says it will work more closely with the US and other democracies on sharing intelligence and protecting its citizens overseas.

Outlook: Taiwan will press allies for a joint response while the US case moves through the courts, adding fresh friction with Beijing.