AirDroid is one of the most popular remote control and management applications for Android phones in the world. It allows you to connect to an Android smartphone from your computer and then transfer files, mirror the screen or only notifications, back up data, or even control various functions of the portable device right from the desktop. You can connect the two via a wireless network or even over the Internet, using 3G/4G mobile data connection, and a free AirDroid account.
AirDroid is impressively powerful, comprehensive and feature-rich. One of my favorite functionalities that this tool provides is the fact that it lets you view the notifications you receive on your mobile phone on your desktop as well, so if you can't find or hear your phone and you receive a message or a call, you can still see that on your computer's screen. It also lets you transfer files between the phone and the computer, so if your USB cable is no longer working, you can use this tool in order to move the photos, videos, music or documents around. Another cool feature offered by this awesome application is the fact that it can lock a lost phone, or even help you find it, locating it on a map (useful in case it got stolen), or making it ring (useful in case you forgot where you put it). It also lets you manage and back up contacts, SMS messages, and the call history of your phone, from your computer. Furthermore, you can send messages from your phone using your computer's keyboard, or simply control any of your phone's function with the mouse thanks to the embedded AirMirror screen mirroring function. The AirMirror function should work only on rooted devices and a few more certified devices. Luckily my HTC Desire 820 seems to be one of the few unrooted devices that are supported (even though it wasn't officially listed as one), as I can use this function perfectly fine with this phone, but that's not also the case with my SO's Xperia M2.
Using your AirDroid account, you can access your phone from any location with Internet access, so you don't have to always be near a computer where AirDroid is installed in order to access your phone remotely. Just login with your AirDroid account on the web.airdroid.com page and you can control your phone remotely from there.
Since AirDroid is a favorite tool of mine, I'm using it for quite a while and I had the time to discover a few minor flaws as well. One of them is the fact that sometimes notifications are lagging, and this could lead to awkward situations, like when you don't see important messages on time, or worse, when messages that you deleted from the phone will still be shown for a short while on the computer's desktop. Another small drawback is the fact that the interface of the desktop client is far from being intuitive and easy-to-use, especially when multiple smartphones are connected to the same AirDroid account. It might take you a while to find out where each function, feature, and setting can be found.
Anyway, despite its small downsides, AirDroid remains the best tool of its kind that one can find at the moment, in my humble opinion. It it gets its client's interface refurnished and improved, it may become truly unrivaled.