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Websites ranging from Facebook, Twitter and Google to parenting message boards and blogs could be fined or blocked if they fail to remove "online harms". That could be material like terrorist propaganda, child abuse, so-called "revenge pornography" and fake news. The government says "the era of self-regulation is over" and it wants to create a new independent watchdog and a code of practice for tech companies. Senior executives could be held personally liable for breaches.
Pressure to act grew after the suicide of 14-year-old Molly Russell - her father partly blames Instagram for her death. There was also criticism levelled at social media firms for failing to take down material posted by the Christchurch mosque gunman.
The plans - now being put out to consultation - have been welcomed by children's charities and police, but free speech campaigners accused the government of "leading the Western world in internet censorship". BBC technology correspondent Rory Cellan-Jones says the trickiest issue could be how the regulator would rule on material that is not illegal but may still be considered harmful - for example, misinformation spread by anti-vaccine campaigners.
Read our guide, Own It, designed to help you and your kids stay safe online.
White House exit
Donald Trump's Secretary of Homeland Security Kirstjen Nielsen has resigned. She was responsible for implementing the proposed border wall with Mexico and the controversial policy of separating migrant families. She gave no reason for her departure, but Anthony Zurcher, BBC senior North America reporter, says the president viewed her as not aggressive enough and her exit suggests he plans to adopt an even more confrontational approach to border security in future. But Prof Sherie Bebitch Jeffe, from the University of Southern California, told BBC Radio 5 Live that having both an acting defence secretary and now an acting homeland security secretary was a projection of weakness for the president on the world stage.
The BBC's Tara McKelvey has looked at the tightrope Ms Nielsen faced in the role. See who else has walked through the White House revolving door here.
The government is expected to reveal in May whether it will allow Chinese telecom giant Huawei to be involved in the next generation of 5G mobile networks in the UK. Now though, Dr Ian Levy - a senior cyber security expert at intelligence agency GCHQ - has told BBC Panorama the company's "shoddy" engineering practices could see its equipment banned from Westminster and other sensitive parts of the UK. Huawei has promised to address concerns, but Dr Levy says he's yet to be convinced.
Four things to know for the week ahead.
'She vanished off the face of the earth'
By Mark Shields, BBC News
It's a horror every parent dreads: the disappearance of a child. But the passage of a half a century since 13-year-old April Fabb vanished has done nothing to ease the pain felt by the community where she lived - nor the terrible fascination with finding the answer which, 50 years on, may still lie in their midst. It was the Easter holidays and the 13-year-old planned to ride the two miles from her sleepy Norfolk hamlet to her sister's house, excited at delivering a birthday present of 10 cigarettes to her brother-in-law. But April never arrived.
What the papers say
Theresa May appears on a number of front pages after she reached out to the public in a video message on Brexit. The Guardian says that while the "homespun video" was praised for its conversational style, there are increasing expectations that cross-party talks will come to nothing. The Daily Express says the message has infuriated Tory hardliners who believe she is set to rip up her Brexit red lines and accept a customs union with the EU. Writing in the Daily Telegraph, Boris Johnson says agreeing to that would be a big step towards "economic serfdom", but the Daily Mail thinks that while it would be a "bitter pill to swallow", changes could be made once the UK is out of the EU. Elsewhere, there's broad welcome for the government's proposals to improve internet safety. The Sun says the crackdown on the "social media Wild West" is better late than never.
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