US tech giants Google, Apple, Facebook, Amazon and Microsoft have been accused of not paying enough taxes, stifling competition, stealing media content and threatening democracy by spreading fake news.
A European Union court on Wednesday rejected a Google appeal against a €2.4-billion anti-trust fine.
Here is how the bloc has tried to regulate Big Tech:
Nobbling competition
The digital giants - collectively dubbed GAFAM - are regularly criticised for dominating the market by elbowing out rivals.
The EU has slapped a total €8.25 billion in fines on Google for abusing its dominant market position across several of its products.
The European Court of Justice in Luxembourg on Wednesday confirmed a €2.4-billion fine imposed on Google by the EU Commission in 2017 for abusing its power over its rivals in online shopping.
It rejected the US search engine giant's appeal, saying ruling that the Commission was right and "Google departed from competition on the merits."
Microsoft was fined €561 million by the EU in 2013 for imposing its search engine Internet Explorer on users of Windows 7.
Amazon, Apple and Facebook are also the targets of EU probes for possible violations of competition rules.
The EU has also unveiled plans for mammoth fines of up to 10% of sales on tech firms that break competition rules, which could even lead to them being broken up.
Taxation
Germany, France, Italy and Spain won a major victory in June when the Group of Seven (G7) agreed to a minimum global corporate tax rate of at least 15% mainly aimed at the tech giants.
For years they have paid little or no tax through complex tax avoidance schemes.
In one of the most notorious cases, the European Commission in 2016 found that Ireland granted "illegal tax benefits to Apple" and ordered the company to pay €13 billion plus interest to the Irish taxpayer.
After an EU court later ruled in favour of Apple, the Commission turned to the European Court of Justice to appeal.
The following year, Amazon was told to pay back €250 million to Luxembourg over similar abuses there.
Personal data
Tech giants are regularly criticised over how they gather and use personal data.
The EU has led the charge to rein them in with its 2018 General Data Protection Regulation, which has since become an international reference.
They must ask for consent when they collect personal information and may no longer use data collected from several sources to profile users against their will.
Amazon was fined €746 million in July by Luxembourg authorities for flouting the EU's data protection rules.
After having fined Twitter nearly half a million euros, the Irish regulator opened a probe into Facebook in April after the personal data of 530 million users was pirated.
France has also fined Google and Amazon a total of €135 million for breaking rules on computer cookies.
Fake news and hate speech
Social networks are often accused of failing to rein in misinformation and hate speech.
The European Parliament and member states agreed to force platforms to remove terrorist content, and to do so within one hour.
EU rules now also forbid using algorithms to spread false information and hate speech, which some major platforms are suspected of doing to increase ad revenue.
Paying for content
GAFAM are accused by media outlets of making money from journalistic content without sharing the revenue.
To tackle this an EU law in 2019 created a form of copyright called "neighbouring rights" that would allow outlets to demand compensation for use of their content.
After initial resistance, Google signed agreements to pay for content with several French newspapers last year, a world first.
However, it did not stop the company being fined €500,000 by France's competition authority in July for failing to negotiate "in good faith" with news organisations. Google has appealed.