LONDON - The inauguration of Joe Biden represents not only a new chapter for the United States, but for the world. For allies and adversaries alike, new relationships with the world's superpower are already taking shape.

In much of Europe, there is a mood of optimism.

"After Joe Biden was elected, you could hear a collective sigh of relief going through European corridors of power," said Rem Korteweg, foreign policy analyst at the Clingendael Institute in the Netherlands. "The climate agenda, global trade policy, multilateral institutions and European security are very much on the top of the agenda of European leaders when it comes to talking to Joe Biden. He is a very strong supporter of the transatlantic security relationship and is a steadfast supporter of NATO."

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Such soothing sentiments in Europe follow four turbulent years of transatlantic relations with President Donald Trump at America's helm. However, there could be a big hurdle ahead: China.

Earlier this month, the European Union agreed in principle to an investment deal with Beijing, despite concerns in both Europe and the U.S. over Chinese trade practices and human rights abuses.

"Europe doesn't see China as a geopolitical peer competitor, not the way the U.S. does," notes Korteweg, who says that over the past four years, many Europeans have begun to question their reliance on the United States.

"They think they need to develop their own so-called 'strategic autonomy.' And the Americans will insist on saying, 'Look, we're back. We're at the head of the table again. Please follow us.' And it's going to require trust-building and good choreography to ensure that the Americans and the Europeans don't end up at loggerheads over such an important issue as how to deal with China," he said.

European Commission President Ursula von der Leyen, European Council President Charles Michel, German Chancellor Angela Merkel, French President Emmanuel Macron and Chinese President Xi Jinping hold a video conference, Dec. 30, 2020.

Meanwhile, European trade with the U.S. is stumbling. Under Trump, the United States and Europe slapped tariffs on some imports of each other's goods. French Economy Minister Bruno Le Maire said this week that Europe would try to end spiraling tit-for-tat tariffs.

"At the top of the agenda will be to clearly say 'stop' to the trade war between the U.S. and Europe. 'Stop' to the sanctions from the U.S. administration on French vineyards, for instance. 'Stop' to the Boeing-Airbus case, which is clearly not in the interest of neither the U.S. nor European countries," Le Maire told reporters.

Britain has traditionally been seen as the transatlantic bridge between the U.S. and Europe. But its ties to the EU have been cut by Brexit.

"So, when it comes to trade issues, or perhaps also climate change or areas of economic regulation, or dealing with financial crises, the United Kingdom is not going to be America's first port of call," Korteweg said.

Biden has in the past been a vocal critic of Britain's exit from the EU. Britain insists its "special relationship" with the U.S. will be unaffected, and analysts say London remains a key security partner for Washington. Britain is due to host the G-7 meeting in June, and the COP26 climate summit in November.

In this photo made available by 10 Downing Street, Britain's Foreign Secretary Dominic Raab gestures during a coronavirus media briefing at 10 Downing Street, in London, April 16, 2020.

British Foreign Minister Dominic Raab said Tuesday reviving the Iran nuclear deal, or JCPOA, from which the U.S. withdrew in 2018 under Trump, is a top priority.

"It is welcome that President-elect Biden and the new administration has talked about coming back into the JCPOA, enhancing and strengthening it," Raab told British lawmakers.

Meanwhile, the coronavirus pandemic has brought health and economic crises to both Europe and the United States. In the near term, analysts say dealing with the deadly health emergency will likely take priority on both sides of the Atlantic.