While the BlackBerry Priv in some forms has already received Android 6.0.1 Marshmallow, and in some other forms may be waiting quite some time, those who favor a physical keyboard and happen to be on T-Mobile's network have been hearing news of an upcoming update and a beta roll out for some time now. Today is the day that the official roll out begins for the final version of Android 6.0.1 Marshmallow on the super-secure keyboard phone. According to the T-Mobile's software update announcement, the dust will settle by the end of the day on June 17, when all Priv smartphones on the network should have received their update. The update should come automatically, but is available through a manual update check as well.
The update brings all of the usual trappings of Marshmallow. Users will enjoy Doze, adoptable storage for their microSD slot, permission management, Google Now On Tap, and tons more Material Design, including all of the nifty animations that were introduced with the current second newest version of Android. Some security enhancements and bug fixes are also on board to help with performance and battery life. Rounding out the update, of course, is the obligatory bringing up to date of the phone's monthly security patch, though T-Mobile's announcement does not make it clear if users will receive the still up-to-date May patch or the fresh-from-the-oven June patch. Given the phone's focus on security, the latter seems as though it would be the most likely.
For the update to be applied, your device should have at least 1.6GB of free space available. The file is only a 1.3GB download, but will need some extra space for files to extract and be moved about. As with any other Android system update, you'll need to have a decent amount of battery charge in order to apply it; T-Mobile's release specifies that 50% battery life is required. The update should be completely rolled out by the 18th of June, so if you don't have your update by then, try a manual update by going into your settings, then About Phone, then System Updates. If it is not available at that point, a reboot may do the trick and, if not, T-Mobile should be able to help.