Android is very specific about company-owned vs personally-owned phones. Personally-owned lets you setup devices with a work profile where very little non-work data is available to the employer. They don't know your personal apps, they dont know your IP address, and they dont know where these apps go (ie no personal network logs). They have no access to these either.
Even for company-owned devices (which require a specific setup, if you bring in your own device that means factory reset and things like hitting 7x the white screen on the first new setup page), the mobile device management api doesn't give you all that much. There's no remote access/rootkit, you can't see private messages (they can see messages you send over a work chat app they own, so if its google hangout chat f.e., by looking at the hangout service itself)
Here are the different modes: https://developers.google.com/android/work/terminology and you can follow the API links to see what they do if you want to verify what I just wrote.