Business Insider has post that Twitter is finally close to doing something about harassment on its social platform. Not a real big move, mind you, but it's good enough to be called a first step given how little it has in way of stopping harassment.
For Twitter, this could only have happened if it realized that users are not happy with what's going on. As an avid Twitter user, I can understand the plight others have been through trying to express themselves only to be harassed (to put it mildly in some cases). Earlier during the Gamergate exploded and some began harassing critics, mostly women (there's more on it here on wiki).
The problem I see is that while Twitter might succeed in shutting down accounts of the perpetrators, it's simply for the bad elements on Twitter to eventually create new accounts to start up their attacks again.
Because Twitter response has been lacking, there are third party and crowd-sourced options.
The problem with Twitter is that is it still growing and working on ways to define itself beyond the tweets and their immediate impacts. It has to satisfy investors and keep users engaged and coming back. And given its last financial result, it's possible that Twitter is headed for a peak and slowing growth.
The company is mostly ran by engineers including its CEO, Dick Costolo. Frankly, the issue may be that there isn't a whole lot of "social" understanding beyond coming up with the platform and maintaining it. Most of the time, these engineer executives may simply be blind and lack the understanding of what these harassment and attacks are doing to users.
So, as you can see, any step towards combatting harassment of its own members by others is a good first step for Twitter.