The laws would also force technology companies to delete anything that a person posted when they were under 18.
But perhaps most unusually they would be forced to help controversial government schemes like its Prevent strategy, by promoting counter-extremist narratives.
"In harnessing the digital revolution, we must take steps to protect the vulnerable and give people confidence to use the internet without fear of abuse, criminality or exposure to horrific content", the manifesto claims in a section called 'the safest place to be online'.
The plans are in keeping with the Tories' commitment that the online world must be regulated as strongly as the offline one, and that the same rules should apply in both.
"Our starting point is that online rules should reflect those that govern our lives offline," the Conservatives' manifesto says, explaining this justification for a new level of regulation.
"It should be as unacceptable to bully online as it is in the playground, as difficult to groom a young child on the internet as it is in a community, as hard for children to access violent and degrading pornography online as it is in the high street, and as difficult to commit a crime digitally as it is physically."