Background: I'm looking for an app that lets me control my Android device from my computer.
Sadly, any attempt at Googling this, only yields results for using the Android device as a remote control.
I've been using Pushbullet for some time, which lets me see Android notifications as popups on my computer. It also lets me do some basic stuff, like reply to text messages when they pop up, but this is very limited.
I'm perfectly OK with using a web interface to access the phone. I'm also familiar with VNC, if that's an option.
Huge bonus for any app that lets me control the device using the computer's mouse to simulate taps and swipes.
Android version: 4.4.2
Price range: Any
Security: Any commonly accepted encryption. For VNC alternatives, this is probably a non-issue.
EDIT: What I'm looking for is full remote access. That is, seeing the full screen of my phone, with my computer's mouse simulating touch on the Android device.