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.