Google has just announced on one of its product forums that the Android Wear 5.1.1 update has started rolling out to all compatible smartwatches. The update will be rolled out gradually, and the company says that it might take anywhere between a few days to a few weeks before it reaches your wrist piece.
Android Wear 5.1.1 is a major update to Google's wearable platform, chief among the new features being Wi-Fi support. With Android 5.1.1, smartwatches will be able to connect to wireless networks and stay in sync with your Android smartphone even when the Bluetooth connection is lost. This means that you'll be able to get notifications and access Google's voice search feature when your phone isn't nearby, but the smartwatch is only be able to connect to Wi-Fi networks that the phone has previously authorized.
Other new features included with this update are support for always-on apps, a new gesture for accessing apps and contacts (a left swipe from the watch face), the ability to change the font size, and support for emoji drawing.
Unfortunately, only some Android Wear 5.1.1 smartwatches will be blessed with these new capabilities. Google says that Wi-Fi support will only be enabled on four smartwatches, the LG Watch Urbane (this one was launched with Android Wear 5.1.1 out of the box), the Motorola Moto 360, the Sony Smartwatch 3, and the Samsung Gear Live.
[UPDATE] It seems the LG G Watch R will also receive Wi-Fi support in a future update.
Google's post in the Android Wear Help Forum also says that the update will only roll out to users who are running the latest version of the Android Wear companion app. To make sure you're up to date, find the Android Wear companion app in Google Play and hit the update button. If there's no update button, you should be running the latest version.
source - Google