A while back I wrote a blog post about Mobizen — an app to access your Android device over USB or via a local or remote network connection. Another app that deserves attention in this space is Vysor, which has a similar feature set with a focus on screen mirroring/remote screen.
After (re-)trying it out a few weeks ago, AirDroid is now my current favorite app in this space as I believe it has the widest variety of features as well as highest-quality mirroring options. Like Mobizen, Airdroid has an app for Windows and OS X and a “Chrome App” can be created for use on Linux, or simply https://web.airdroid.com.
Enjoy!