Yes, you can connect over wifi to the phone, and notifications of calls and texts come through when connected via wifi (on the same wifi router only), and I've been able to get email over wifi. Not all apps connect via wifi, though: you get a message from many apps when you try them, telling you to connect via bluetooth. Also, the wifi is hard on the battery in my experience; the only time I've come near to burning through my battery in a single day is when using wifi a lot. And finally, the Gear S2's wifi is limited to open or simple password connections. It can not connect to wifi networks that require more elaborate signons involving things like providing an email address and a password in a browser, or more sophisticated enterprise security systems. So I can not connect my Gear S2 to wifi at work, for example.