Here are some of the sticking points in the relationship between the economic giants:

- Ukraine war -

The EU has called China an "enabler" of the Ukraine conflict due to it refusing to criticise Moscow's invasion and selling goods with both civilian and military uses to Russia.

China rejects this claim, arguing that it is a neutral party to the war that has never sold weaponry to either side.

Their differences were on show last week when the EU included some Chinese firms and financial institutions in its latest package of sanctions designed to thwart the Russian advance.

Beijing said on Monday that the sanctions would have "a serious negative impact on China-EU economic and trade relations".

Several outlets have reported that Chinese foreign minister Wang Yi told the EU's top diplomat this month that Beijing did not wish to see Russia lose the war as it feared the United States would then turn its full focus towards China.

Those comments, reported by Hong Kong's South China Morning Post and citing unnamed EU officials, would run counter to Beijing's public stance on the hostilities.

- Trade imbalance -

Brussels bristles at its yawning trade deficit with China, which stood at around $360 billion last year, according to data from the European Commission.

Although China is the EU's third-largest trade partner, the bloc describes economic ties as "critically unbalanced".

European Commission President Ursula von der Leyen has said she will demand greater market access in talks with Chinese officials on Thursday.

Beijing says Brussels needs to change its mentality and "properly handle divergences and frictions".

- EVs, clean energy -

The EU and China are also locked in a dispute over Beijing's state support for what it deems critical industries, including electric vehicles (EVs) and renewable energy technology.

Brussels argues that Chinese companies in those sectors benefit from unfair government subsidies that allow them to undercut European competitors on prices.

In October, the EU imposed extra import taxes of up to 35 percent on Chinese EV imports. It has also begun a probe into Chinese suppliers of wind turbines.

Beijing has dismissed Brussels' claims and has announced its own investigations into alleged trade distortions by EU suppliers -- from pork to brandy sellers -- widely seen as retaliatory.

It has also lodged a complaint about the EV curbs with the World Trade Organization, which said in April that it would set up a panel to assess the EU's decision.

- Rare earths -

Von der Leyen has said she and European Council President Antonio Costa will ask China to loosen export restrictions on rare earths -- crucial commodities used to manufacture electronics and other goods.

China dominates the global industry for extracting and refining rare earths.

Since April, it has required licences to export some of the strategic materials, triggering anxiety among businesses worldwide.

The European Parliament has condemned the move as "unjustified" and "intended to be coercive", and EU officials have stressed the need to diversify the bloc's supply chain.

China says it needs to control the export of rare earths as they are "dual-use" goods with potential military applications.

Beijing has proposed a "green channel" to ease the export of rare earths to the EU.

- Climate change -

The warming planet is historically an area of convergence between Brussels and Beijing, with both sides signalling a willingness to cooperate on combating climate change.

Even here, though, all is not rosy.

A top EU climate official told the Financial Times this month that Brussels would not sign a joint climate declaration with China until Beijing adopted bolder emissions reduction goals.

An editorial in the state-backed China Daily newspaper then accused the EU of playing the "climate card" to get China to change its position on the Ukraine war.

The EU aims to become carbon neutral by 2050. China -- the world's biggest greenhouse gas emitter -- has pledged to do so by 2060.