President Trump's haphazard war on Chinese tech has left the Biden administration with a raft of unfinished business involving efforts to restrict Chinese firms and products in U.S. markets.

Why it matters: The Chinese and American tech industries are joined at the hip in many ways, and that interdependence has shaped decades of prosperity. But now security concerns and economic rivalries are wrenching them apart.

Here's where things stand between the U.S. and several key Chinese tech powerhouses:

Xiaomi

• In the waning days of the Trump administration, the Defense Department added Chinese phone maker Xiaomi to its a list of companies with ties to the Chinese military, potentially requiring US investors to sell their stake in the company. Xiaomi denies it is owned or controlled by the military.
• Why it matters: Xiaomi doesn’t sell phones in the U.S., but it does have a significant amount of investment from U.S. funds — and also has long-term ambitions of doing more U.S. business.

SMIC

• China’s largest chip foundry was added to the so-called entity list in late December, notably limiting the firm's access to key gear from the U.S., especially equipment used in the newest generation of semiconductors.
• Why it matters: Much of the gear used to turn silicon wafers into chips is made by U.S. companies like Applied Materials. However, the U.S. move against SMIC also hurts global chipmaking capacity during a time of significant shortage.

Huawei

• The Chinese telecom giant remains the tech company most in U.S. crosshairs, facing actions and restrictions from a range of government entities, including the Justice Department, Commerce Department and FCC.
• Huawei is challenging many of these actions in court, including in a recent suit aimed at reversing FCC-imposed restrictions.
• Why it matters: Huawei is one of a handful of companies around the world that make the gear needed for 5G and other cellular networks.
• The company has been particularly successful in developing countries, partly because its equipment often sells for far less than that from rivals such as Nokia, Ericsson and Samsung.
• Huawei has also been a global leader in smartphones, though its ability to compete outside China has been severely curtailed by its lack of access to Google's Android services and other U.S.-developed technology.

TikTok

• Trump's effort to force a sale of the Chinese-owned video-sharing app by imposing a U.S. ban was his noisiest campaign against a Chinese company. But several key components of the effort ran aground in court, and a deadline for a sale came and went with TikTok still in limbo.
• Officials earlier this month said the Biden administration had paused talks initiated under Trump to sell TikTok's U.S. operations to an investor group that included Oracle and Walmart.
• Why it matters: Some lawmakers have suggested Beijing could force TikTok to hand over Americans' data or otherwise somehow exploit the app for spying or hacking purposes.
• The Trump administration didn't turn up any evidence of wrongdoing in making the case that TikTok should be banned, but suggested the risk alone justified its moves.

WeChat

• When Trump issued his order against TikTok, he paired it with a ban on WeChat, the chat app used globally by Chinese speakers. But that bid, too, got derailed in court.
• In his final weeks in office, Trump then sought to ban WeChat Pay from the U.S., together with a number of other Chinese-owned payment platforms.
• Why it matters: WeChat is widely used not only by people in China but among the global Chinese diaspora. Banning it could cut off a critical communications link between people around the world and their relatives and friends in China.

Between the lines: China is running into growing pains of its own in the push to own the future of technology.

• SMIC, for instance, was struggling to deliver on ambitious expansion and production goals even before facing the Trump administration's restrictions.
• Several leading Chinese tech executives have run afoul of Beijing.
• The Chinese government has also embarked on an antitrust crackdown that could clip several domestic tech giants' wings.

The bottom line: The Biden administration now has to sort out which Trump initiatives to drop — because they were botched, thrown out in court or self-defeating — and which can still serve the U.S.'s long-term goals of competing with China and limiting Chinese security threats.