So a lot of us have Smart TVs and Chromecasts that can cast our phone screens to the television, but what about to a laptop/computer?
I came across this conundrum when I was preparing a wedding game and wanted to live feed a video to a projector sceen (so everyone could see), but I didn't have the cables to run a camcorder from the game station to the projector.
I came across Mobizen, which is a pretty handy app/program that can do just that. You just need an Android phone and an email address to set it up on your phone and computer. You can even record video of your phone screen if you want to do tutorials and such.
Like Chromecast, though, there's lag between the paired devices (depends on the resolution, FPS and such that you can adjust) and they have to be on the same WiFi network.
In my case, live feed can also be achieved via a Skype call between phone and computer (you'll need two Skype accounts, of course, and decent WiFi), which ended up being the method of choice.