Sony Mobile has put out a new video showing how to unlock the bootloaders of qualifying Xperia devices. The video goes over exactly how to use the resources set forth in Sony's developer website to unlock the bootloader on approved devices. You can check if your device's bootloader can be unlocked by checking the list on the site, or by using a special developer menu accessed with dialer code *#*#7378423#*#*. If "Root Status" is missing or says no in that menu, than your device cannot have its bootloader unlocked. Otherwise, the video shows how to use ADB and Fastboot with a Sony-supplied bootloader unlock code.
The process has a good number of steps, but is actually fairly simple. Before you start, you'll want to head to your phone's "About Phone" menu and click on your Build Number a few times to unlock the Developer Settings menu, then go in there and make sure that OEM Unlock and USB Debugging are turned on. From there, you can turn off your device for now. If you already have ADB and Fastboot installed on your system, you're good to go, but if not, you can download them from Google's developer website. Windows users will have to set up drivers during this step, while Linux and Mac users should be able to simply install the program. To double check installation of ADB, type "adb devices" into your console of choice. To check for Fastboot installation, type in "fastboot devices". If both of those commands parse, even if they're blank, you're good to go.
From there, go to Sony's page, pick your device from the list, and register your email. You'll receive a link in your email that will bring you to instructions for your device, including how to put it in Fastboot mode, and a code. Once you have that code, connect your device to your computer, turn on Fastboot mode per the instructions on the page, and enter in the commands on the page. Once you've done all of that, your bootloader is officially unlocked, and you're ready to flash custom recoveries and ROMs, at the expense of your warranty.