The European Union and China held a video summit on Monday, their first formal talks since the new European Commission took office late last year. Here are some of the issues:
The EU wants further access to the Chinese market and is concerned the US-China "Phase I" deal, under which Beijing committed to purchase US goods, unfairly discriminates against European companies.
China and the EU are negotiating an investment agreement, with Brussels wanting more access particularly for the auto, biotech, telecoms and computer sectors.
The EU also has concerns about production overcapacity, such as in steel, and wants Beijing to be more engaged on updating global trade rules.
From October, the EU will monitor more closely foreign takeovers in Europe, particularly - although not exclusively - from China, something Beijing has said is protectionism.
Fearful that state-backed Chinese companies are seeking to dominate industries, the Commission is discussing expanding the scope of its screening to include new projects on defence, satellite communications and nuclear energy.
The Commission is also preparing a policy to deal with what it says are the distortive effects of Chinese subsidies in the EU, particularly involving takeovers and in bidding for public tenders, although work is at an early stage.
China contributes more than a quarter of the world's carbon emissions and is one of the few industrial nations where emissions are growing, says the EU.
China is planning to start an emissions trading system, but the system has still not started. Other developing nations are reluctant to move if China does not.
EU officials say China has sought to pressure EU countries that criticise its handling of the novel coronavirus, using social media to spread fake reports of European neglect of Covid-19 patients. Beijing has denied wrongdoing.
The EU is also concerned about investment in EU technology by state-subsidised firms and said it will be particularly vigilant on critical areas such as micro-electronics and artificial intelligence.