The Digital Services Act and Digital Markets Act, which were introduced Tuesday, will give regulators expanded powers to rein in the power of Big Tech and could force companies including Facebook and Google to face steep penalties, including hefty fines or even breakups, if they don't change their business practices.

Together, the new rules amount to the most aggressive legislative effort against tech companies yet.

The Digital Services Act will require platforms to swiftly remove illegal content while providing more transparency to users about why takedowns are happening. It will also require online platforms to verify the identity of sellers in order to make it harder for "dodgy traders to do their business," Margrethe Vestager, executive vice-president of the European Commission and the EU's digital czar, said at a press conference.

The Digital Markets Act will ban the largest tech companies from engaging in a set of behaviors that the EU deems anticompetitive, including blocking users from un-installing any pre-installed software or apps.

Companies that don't follow the Digital Services Act could be fined up to 6% of global revenues, while violations of the Digital Markets Act could result in fines of up to 10% of global revenues.

The proposals are not final, and it will likely be years before the European Union agrees on how the final legislation will look.