From rebuilding the Iran nuclear deal to fighting the pandemic to addressing climate change, Europeans are scrambling to seize the moment with the incoming U.S. leader. Because of Joe Biden’s age and history, many here believe he will be more interested in cooperation with Europe than any U.S. president for the foreseeable future, Democrat or Republican.

But leaders on both sides of the Atlantic warn that some of the irritants of the Trump years will remain, and other divides could still open — especially on what may be the greatest foreign policy challenge of Biden’s presidency, an increasingly aggressive and expansionist Beijing. European countries vary sharply on how they think they should manage relations with China, and the most populous and most powerful country in Europe, Germany, also has the closest trading relationship with Beijing.

European leaders also have become embroiled in an intramural debate about the extent to which they should seek independence from the United States, a goal increasingly pushed by French President Emmanuel Macron and opposed by Germany and others.