I have tried connecting to addresses and ip's with sockets and httpurlconnection with no success, and I do have the Internet permission in the manifest.
I have read that the watch doesn't have to be on the same network where the phone is, so the watch is capable of true Internet connections, but maybe they're not allowed on the apps.
Android Wear does support direct internet connections, but the wifi connection is a bit unstable for me (or maybe it's all the wifi AP's going crazy here at work..)
Yes with the Android Wear 5.1.1 update does support direct internet connections. I haven't found the connection unstable like Filipe but I have found it necessary to have the Bluetooth connection off. Android wear seems to always prefer the Bluetooth connection and will turn off the WiFi if Bluetooth is present. Naturally when Bluetooth is on all the socket connections or other direct connections fail.
When I turn the Bluetooth off on the phone and WiFi is connected on Android Wear any direct connection seems to work just fine.
