Android Wear 2.0 brings a ton of new features and Google has now updated the Android Wear support page with a list of watches that currently have the software, watches that should be getting it soon, and watches that won't be getting an update at all. The second generation Moto 360 and its Sport variant, the LG Watch Urbane 2nd Edition LTE, the Huawei Watch and the Ladies version, as well as the ASUS ZenWatch 2 and ZenWatch 3, are all shown as due for an update to Android Wear 2.0. Google does not give exact dates that updates are expected for each one, instead saying that these smartwatches will be receiving their updates sometime between 'the end of April and late May'. The Huawei Watch is a notable member of that list; it got its update to Android Wear 2.0 last month, but that update was pulled due to a bug.
Among the older watches that won't be getting an update, Google lists the original LG G Watch, the Samsung Gear Live, the Sony Smartwatch 3, the original Moto 360, and the original ASUS ZenWatch. All of these sport 512MB of RAM and most run on a fairly powerful Qualcomm Snapdragon 400 processor, but are all getting a bit long in the tooth, having all been released back in the platform's inaugural year of 2014, save for the fairly young Sony Smartwatch 3, which came out in 2016. Sony confirmed a while back that the Sony Smartwatch 3 would not get Android Wear 2.0, and popular speculation pegged the Broadcom processor as the cause.
The page also contains a handy list of all Android Wear 2.0 smartwatches currently available, whether they had the software when they first came out, like the LG Watch Sport, or got it via an update, like the Tag Heuer Connected. Instructions for those smartwatch owners who are awaiting the update are pretty simple; just ensure that the watch is on its charger overnight, while paired up to an Android phone, with the newest version of the Android Wear app. Google rounds out the support page by stating that all new Android Wear smartwatches coming out from here on will come running on Android Wear 2.0.