British Prime Minister David Cameron has called for a boycott of sites that allow cyberbullying, while asking for website operators to "step up to the plate" and show some responsibility.
A number of companies have pulled their ads from Ask.fm, the site where 14-year-old Hannah Smith was bullied before she committed suicide.
British MP Barry Sheerman wants to take action. On News Stream he said, "I would set up a commission and look at the responsibility of people who own and manage sites like Twitter and Ask.fm because they have responsibility."
"I would look at a range of options like a red button if you're being bullied, so immediately it flags you to a counselor - if you are a child - who can give you information, guidance and advice."
"Also, what we need to do is prosecute these people who cause an enormous disturbance to others as much mentally as physically."
Click on to hear more from Sheerman. What he reveals could be the beginning of one country's legislated approach to online abuse.
After a dark week for women on social media, many are asking: What do you do if you become the target of online abuse?
Laura Bates, founder of the Everyday Sexism Project, offers some practical advice.
She recommends keeping your address and phone number off the Internet, as well as reporting any abuse to the social platform.
As for Twitter, an in-tweet report button is available on Apple devices and will be available for Android and Twitter.com next month.
"And if somebody threatens you with rape online, death threats," says Bates, "you can and should go to police."
Threatening to rape or kill someone is a crime. Even on social media.
Should Facebook or Twitter do more to clean up their platforms from bullying or direct threats?
Yes... and no, says News Stream contributor Nicholas Thompson.
In the case of Twitter, he says its in-tweet report abuse button might be the best way for the network to deal with online abuse.
"It allows Twitter to self-police without Twitter taking the extreme step of saying, 'we're going to ban this kind of speech'... which always gets you into some kind of trouble," Thompson says.
"Twitter's general policy needs to be to let more speech happen. It shouldn't get in the business of restricting speech except in extreme and particular circumstances."
Click the video above for more of our conversation about encouraging expression while discouraging the trolls.
Catch News Stream with Kristie Lu Stout weekdays at 8pm HKT/ 12pm GMT / 8am ET on CNN International.