The United States has tried, with some success, to halt China’s progress with artificial intelligence amid concerns that the technology is helping modernize the Chinese military.

U.S. officials have set up one of the most extensive tech blockades ever attempted, banning the export to China of advanced A.I. chips, which are primarily made by Nvidia, a Silicon Valley firm that is one of the world’s most valuable companies.

But given the vast profits at stake, businesses around the world have found ways to skirt the rules, an investigation by The New York Times has found.

Interviews with more than 85 current and former U.S. officials, executives and industry analysts, as well as reviews of corporate records and visits to companies in Beijing, Kunshan and Shenzhen, showed that there is an active trade in restricted A.I. technology in China — part of a global effort to help China circumvent U.S. national security restrictions.

Here are some takeaways from our investigation.

An underground marketplace of smugglers is funneling A.I. chips into China.

The Times spoke with representatives of 11 companies in China that said they sold or transported banned Nvidia chips, and found dozens more businesses offering them online.