In 2011, with the help of Bitch magazine, a young media critic named Anita Sarkeesian hosted a Web-video series called “Tropes vs. Women.” Over six segments, she critiqued archetypes of females in film, comic books, and TV, from the bubbly so-called Manic Pixie Dream Girl to the wild-eyed Evil Demon Seductress and the self-serious Straw Feminist. The following spring, Sarkeesian launched a Kickstarter campaign for a project called “Tropes vs. Women in Video Games,” to delve into what she saw as the objectification of women in gaming culture, where skimpy armor and bulbous breasts abound. (Developers have even bragged about how they have perfected the physics of female curvature by going “hands on.”) Sarkeesian aimed to raise six thousand dollars for her project; after thirty days she had accumulated $158,917 from nearly seven thousand donors.

To conscientious parents, or just casual observers of the current video-game landscape, the overwhelming support for Sarkeesian’s project may come as no surprise. What was surprising, however, was the intensity of the reaction from some of the Web’s more caustic pockets, like Reddit’s Men’s Rights forums.

Sarkeesian, a Canadian-American of Armenian descent, became the target of a stream of Internet harassment, which included hateful words for Jews, blacks, and gays. Her Wikipedia page was edited to state that she was a “hooker who focuses on drugs in popular culture and their associations with tropes.” Bunitar Sarkereszian, as the Wiki-vandals renamed her, also “holds the world record for maximum amount of sexual toys in the posterior.” Abusive video gamers (called griefers) doctored pornographic images of Sarkeesian, while others tried to hack into her accounts, get Kickstarter to ban her project, flag her YouTube videos as terrorism.

Sarkeesian’s Web site, called Feminist Frequency, posted comments left on the YouTube video that she had created for her Kickstarter page. They included: ”Would be better if she filmed this in the kitchen”; “I hate ovaries with a brain big enough to post videos”; “She is a JEW”; “I hope you get cancer :)”; “I’ll donate $50 if you make me a sandwich”; “The bigger the hoops, the bigger the whore.”

On Feminist Frequency, Sarkeesian recounted, “There was even a game made where players were invited to ‘beat the bitch up’ in which upon clicking on the screen, an image of me would become increasingly battered and bruised.” Griefers also collected and distributed her personal information and sent warnings of violence through every social-media channel: threats of death, sexual assault, and rape.

This past Sunday, Sarkeesian tweeted, “I’ve reported numerous rape threats to @Twitter. This is how they respond: “The account is currently not in violation of the Twitter Rules.” Less than an hour later, she posted a screen grab of one such tweet, showing the account @CoolDehLa tweeting, on December 26, 2012, “@femfreq I will rape you when i get the chance.” Sarkeesian wrote, “Twitter says ‘We have found the reported account is currently not in violation of the Twitter Rules at this time.’ ” Sarkeesian’s two tweets were retweeted more than seven thousand times. On Monday morning, @CoolDehLa’s user page could not be accessed—the account had been suspended.

The same weekend, an even bigger Twitter brouhaha flared up across the Atlantic. Caroline Criado-Perez, also a feminist activist and blogger, had played a significant role in the Bank of England’s decision to put a non-royal woman on the British banknote. As soon as the Bank decreed that Jane Austen’s likeness would be featured on ten-pound note, Criado-Perez was subject to an online onslaught. In her words, she received “about 50 abusive tweets an hour for about 12 hours.” It was so many, she tweeted, that “I actually can’t keep up with the screen-capping & reporting—rape threats thick and fast now. If anyone wants to report the tweets to Twitter.”

A petition began circulating to make it easier to report abuse on Twitter, demanding a “zero tolerance policy on abuse”; by now, over a hundred thousand people have signed it. A Labour MP named Stella Creasy published an op-ed defending Criado-Perez in the Guardian this weekend, headlined, “Twitter’s inadequate action over rape threats is itself an abuse.” Shortly after it went live, she began to receive rape threats herself. One warned, “YOU BETTER WATCH YOUR BACK….IM GONNA RAPE YOUR ASS AT 8PM AND PUT THE VIDEO ALL OVER THE INTERNET.” The attacks led to a proposal, from the popular feminist and columnist Caitlin Moran, for a Twitter “Trolliday,” a day when Internet trolling is especially discouraged. On Sunday, Scotland Yard arrested a twenty-one-year-old man in Manchester in connection with a deluge of hostile tweets threatening to rape and kill Criado-Perez, delivering a measure of legal recourse.

On Monday, Twitter responded to the uproar on its U.K. blog. “We Hear You,” it wrote, in the same pal-to-pal tone that other capitalist giants of the start-up era often choose to employ. The press release, signed by Del Harvey, the senior director of trust and safety, stated, “We are not blind to the reality that there will always be people using Twitter in ways that are abusive and may harm others. While manually reviewing every Tweet is not possible due to Twitter’s global reach and level of activity, we use both automated and manual systems to evaluate reports of users potentially violating our Twitter Rules.” Twitter also reminded users of a relatively new feature allowing them to report individual tweets from its iPhone app, and says that it plans to make the feature available on Android and on desktops.

As Jeffrey Rosen outlined in The New Republic, Twitter pursues the John Stuart Mill-infused “American free-speech ideal” (as opposed to the European stance, which, owing to its history of Fascism, regards suppressing hate speech as a means of promoting democracy) more powerfully than the other social-media tech giants. Twitter, writes Rosen, has “explicitly concluded that it wants to be a platform for democracy rather than civility.” The company doesn’t ban hate speech at all.

Twitter’s official policy on violence and threats is, simply, “You may not publish or post direct, specific threats of violence against others.” For Twitter, the question of when to intervene comes in gauging what is “direct” and what is “specific.” Tweeting, “You promised you would not check out the new Kanye for APC line without me I am going to kill you!!” is different than saying, “When you get home tonight, I’m going to break into your apartment and put a bullet through your head.”

I asked Harvey how directness and specificity are measured by the company. She explained that if two accounts levy abuse at each other equally, that can considered bad behavior more than abuse and harassment. The clarity of the threat, she told me, is what Twitter examines. If a user makes a specifically violent threat, Twitter will remove the threat, or even the user. Accounts that exist only to promote hate, exclusively tweeting “you deserve to die”-type messages, are barred. (It also encourages users to contact law enforcement if they receive specific threats. Suspension of an account, after all, can’t stop a criminal en route to your house.) But if you are a woman who has received repeated threats of rape, even “indirect” threats—maybe even ones meant as a joke—may feel pretty darn direct.