How to enable the new Gmail in a web browser
Next you'll be asked which tabs you want to use -- primary, social and promotions are checked by default; updates and forums are other options. Once enabled, you'll find e-mails sorted among the tabs. To move e-mails between tabs, just click and drag. (You'll also be asked if you want to continue to get that particular kind of e-mail in the new tab.)
Still no sign of the new Gmail app for Android, which also will bring a new sorting experience.