Big tech firms face yearly checks on how they are tackling illegal and harmful content under new rules unveiled by the European Commission.
Fresh restrictions are also planned to govern their use of customers' data, and to prevent the firms ranking their own services above competitors' in search results and app stores.
The measures are intended to overhaul how the EU regulates digital markets.
Large fines and break-ups are threatened for non-compliance.
It is proposed that if companies refuse to obey, they could be forced to hand over up to 10% of their European turnover.
And "recurrent infringers" are warned that they could be made to divest "certain businesses, where no other equally effective alternative measure is available to ensure compliance".
The two new laws involved - the Digital Services Act and the Digital Markets Act - have yet to be passed, so would only come into force after the Brexit transition period has ended.
The UK's own regulator - the Competition and Markets Authority - announced its own plans to place limits on the tech giants last week, and ministers have just detailed how they plan to tackle online harms.
The European Commission's press conference was scheduled for the afternoon to allow tech leaders on the US's West Coast to watch live, but began later than originally advised.
Competition Commissioner Margrethe Vestager described the two laws as "milestones in our journey to make Europe fit for the digital age... we need to make rules that put order into chaos".
Internal Market Commissioner Thierry Breton added that the laws had been designed to be applied "very quickly" once they came into effect.
The focus of the Digital Services Act is to create a single set of rules for the EU to keep users safe online, protect their freedom of expression and help both them and local authorities hold tech companies to account.
It introduces a sliding scale, under which firms take on more obligations the larger and more influential they are.
So, for example, all internet companies must provide users with a way of getting in touch and the means to see their terms and conditions.
The operators of online platforms - such as social media apps and video-sharing sites of any size - must prioritise complaints raised by "trusted flaggers", who have a track record of highlighting valid problems.
Likewise, all online stores must be able to trace traders selling goods via their platforms, in case they are offering counterfeit items or other illegal products.
"[It] will require online marketplaces to check their sellers' identity before they are allowed on the platform, which will make it so much more difficult for dodgy traders to do their business," commented Mr Breton.
But the biggest players must also subject themselves to further scrutiny, including an annual independent audit to check they are following the rules.
In addition, once a year they must publish a report into their handling of major risks, including users posting illegal content, disinformation that could sway elections, and the unjustified targeting of minority groups.
Suggested counter-measures include preventing abusive users earning money from ads, and checking moderator guidelines is kept up-to-date.
Furthermore, the law specifies that local officials can send cross-border orders to make tech firms remove content or provide access to information, wherever their EU headquarter is based.
A commission spokesman gave the example of Amsterdam's local government being able to ask a service like Airbnb, which is based in Dublin, to remove a listing of a non-registered apartment and share details about a host suspected of not paying taxes.
The Digital Markets Act centres on the regulation of "gatekeepers" - those behind "entrenched" services that other businesses use to provide their own products.
This covers the operators of search engines, social networks, chat apps, cloud computing services and operating systems, among others.
They are likely to include Google, Facebook, Apple, Amazon and Microsoft.
The idea is to prevent the firms gaining unfair advantages via their elevated positions.
The new rules include obligations to:
- inform the regulator of any planned takeover of another service
- not treat their own service more favourably than rivals' when deciding which order to show them on screen
- not use data gathered via their main service to launch a product that will compete with other established businesses
- let users uninstall pre-installed apps on their platform and use different software
The commission would be able to issue fines of up to 10% of a firm's annual turnover in Europe under the Digital Services Act, and 6% under the Digital Markets Act.
Facebook was one of the first to respond, saying it thought the laws were "on the right track to help preserve what is good about the internet".
But it also took the opportunity to call attention to one of the other US tech giants.
"We hope the Digital Markets Act will set boundaries for Apple," said a spokesman.
"Apple controls an entire ecosystem from device to app store and apps, and uses this power to harm developers and consumers, as well as large platforms like Facebook."
Apple declined to respond.
Google later sounded a more cautious note.
"We are concerned that [the laws] appear to specifically target a handful of companies and make it harder to develop new products to support small businesses in Europe," said Karan Bhatia, its vice president of government affairs.
The DigitalEurope trade association also voiced concern about whether the commission had got the balance right between privacy and preventing harmful activities, but said it needed more time to read the details.
The tech giants and digital rights campaigners are among those likely to try to influence their final shape of the two laws.
But if passed, they should update current rules, which date back to 20 years ago when some of the tech firms affected did not exist.
And they may influence other regulators - in the US and elsewhere - which are also planning to introduce new restrictions of their own.