To find this setting, navigate to your Settings page by clicking the gear icon at the top. Scroll to the "Content" subhead on that page -- listed under "Account" -- and find the "Messages" section. By default, the new option is opt in. It reads, "Generally, you must follow someone before they have the ability to direct message you. If you check this option, any Twitter user that follows you will be able to send you a DM, regardless of whether you decide to follow them back." Check the box to opt in and click "Save changes" at the bottom.
This new setting has pros and cons: If you work in a profession in which you're frequently messaged through @ replies requesting a follow-back so someone can message you privately, this new feature removes that barrier, making you more accessible to others. An obvious negative is the potential to receive an influx of unwanted or poorly targeted messages, clogging your inbox (and your phone, if you receive direct message alerts via text).
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Enabling direct messages from all Twitter users may not yet be applicable to your account. Twitter is reportedly slowly rolling out the new setting to everyone.
This feature will likely be most appealing to brands and businesses, which can open up another channel of communication with customers to help resolve issues by responding privately. The inability to communicate privately with customers was highlighted earlier this year when a frustrated British Airways passenger tweeted the airline to complain that it had lost his father's luggage. The airline requested that the user send it a direct message, however the customer was unable to do so because the airline did not follow him.
In the last several months, Twitter has launched a number of updates and new ventures, including a partnership with a handful of television networks to integrate tweets into programming. Most recently, the social network relaunched Twitter Alerts, an emergency alert feature that messages users via push or SMS. It also rolled out related headline links, which add more context to newsworthy tweets, as well as push notifications for personalized recommendations for people to follow based on who others in your network have added recently.