If you have a newer Samsung device, you can install SideSync and that lets you view and control your phone on a PC. But yeah, this only works for Samsung devices. This app also lets you share your keyboard/mouse with the phone even if you're not seeing the screen on your PC.
As for Teamviewer, although I've never used it, it's not the first time someone suggests using that to view and control an Android device on a PC, so it must work...but as some posters before have stated, you might need a different 'element' and to have your device supported.