The social media giant has made some efforts this year to use technology to flag abusive tweets without the need for human intervention. While such algorithm-assisted policing can work, they also flag plenty of false positives and miss a lot of filth. Twitter has also tested a "hide replies" feature and made it easier to report abusive tweets.
Still, much of the abuse and vitriol on Twitter comes in the form of direct messages from perfect strangers -- many of which users may not even follow. Women and people of color are particularly subject to this form of online harassment. If your account is set up to accept direct messages from anyone, Twitter will file messages from users you don't follow in a folder called "message requests." It also has a "quality filter" that will weed out what it defines as "lower-quality" messages from your message requests folder entirely. You won't be able to see the suspect messages unless you unselect the quality filter.
This latest filter for sensitive content by Twitter is a bit of a happy middle ground. The first few lines of suspect messages will be hidden and replaced with the line, "This message is hidden because it may contain offensive content." You can then choose to either view or delete them. This way, you won't miss the odd NSFW missive from an old sorority sister or the awkwardly written message from a random business contact.