The Galaxy Note 4 and Note Edge both came out a year ago, a time when manufacturers still shipped their devices running Android KitKat. Owners eventually got to experience Lollipop in a later update, and as we've seen from Sprint and AT&T, carriers have started pushing devices up from Android 5.0.1 to 5.1.1. You can now add T-Mobile to that list.
The over-the-air update pushes the Note Edge to build number N915TUVU2COK2 and requires a 150MB download. The Note 4 leaps to either N910TUVU2DOK2 (677.68MB) or N910T3UVU1DOK2 (223.28MB).
For both devices, this release also introduces Advanced Messaging and Video Calling, which are only useful if you're corresponding with someone else who is on T-Mobile and has a compatible device. Hit up the source links below for the official changelogs.