The US State Department said Tuesday it would deny visas to a former EU commissioner and four others, saying they "have advanced censorship crackdowns by foreign states -- in each case targeting American speakers and American companies".

Trump has vowed to punish countries that seek to curb US big tech firms.

Brussels has adopted a powerful legal arsenal aimed at reining in tech giants -- namely through its Digital Markets Act (DMA) which covers competition and the Digital Services Act (DSA) on content moderation.

The EU has already slapped heavy fines on US behemoths including Apple, Meta and X under the new rules.

Here is a look at the EU rules drawing Trump's ire:

- Digital Services Act -

Rolled out in stages since 2023, the mammoth Digital Services Act forces online firms to aggressively police content in the 27 countries of the European Union -- or face major fines.

Aimed at protecting consumers from disinformation and hate speech as well as counterfeit or dangerous goods, it obliges platforms to swiftly remove illegal content or make it inaccessible.

The law instructs platforms to suspend users who frequently share illegal content such as hate speech -- a provision framed as "censorship" by detractors across the Atlantic.

Tougher rules apply to a designated list of "very large" platforms that include US giants Apple, Amazon, Facebook, Google, Instagram, Microsoft, Snapchat and X.

These giants must assess dangers linked to their services regarding illegal content and privacy, set up internal risk mitigation systems, and give regulators access to their data to verify compliance.

Violators can face fines of up to six percent of global turnover, and the EU has the power to ban offending platforms from Europe for repeated non-compliance.

Elon Musk's X was hit with the first fine under the DSA on December 5, a 120-million-euro ($140 million) penalty for a lack of transparency over what the EU calls the deceptive design of its "blue checkmark" for supposedly verified accounts, and its failure to provide access to public data for researchers.

- Digital Markets Act -

Since March 2024, the world's biggest digital companies have faced strict EU rules intended to limit abuses linked to market dominance, favour the emergence of start-ups in Europe and improve options for consumers.

Brussels has so far named seven so-called gatekeepers covered by the Digital Markets Act: Google's Alphabet, Amazon, Apple, TikTok parent ByteDance, Facebook and Instagram parent Meta, Microsoft and travel giant Booking.

Gatekeepers can be fined for locking in customers to use pre-installed services, such as a web browser, mapping or weather information.

The DMA has forced Google to overhaul its search display to avoid favouring its own services -- such as Google flights or shopping.

It requires that users be able to choose what app stores they use -- without going via the dominant two players, Apple's App Store and Google Play.

And it has forced Apple to allow developers to offer alternative payment options directly to consumers -- outside of the App Store, hitting it with a fine of 500 million euros in April.

The DMA has also imposed interoperability between messaging apps WhatsApp and Messenger and competitors who request it.

The EU fined Meta 200 million euros in April over its "pay or consent" system after it violated rules on the use of personal data on Facebook and Instagram.

Failure to comply with the DMA can carry fines in the billions of dollars, reaching 20 percent of global turnover for repeat offenders.

- RGPD and AI -

The EU's data protection rules (RGPD) have also tripped up US tech giants, with Brussels issuing numerous fines since they came into force in 2018.

The rules require firms to seek the consent of users to collect personal data and to explain what it will be used for, and gives users the right to ask firms to delete personal data.

Fines for violations can go as high as 20 million euros, or four percent of a company's global turnover.

The EU has also adopted its AI act which will gradually bring in guardrails on using artificial intelligence in high-risk areas such as security, health and civic rights. In the face of pressure from the industry, the EU is considering weakening the measures and delaying their implementation.

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