Via EDL / Download Mode - If none of the methods above work (bypasses bootloader, only works on Qualcomm-based devices)

Make sure you run 64-bit Windows 7 or later.

Disable Driver Signature Verification on Windows. Instructions here.
http://www.howtogeek.com/167723/how-to-disable-driver-signature-verification-on-64-bit-windows-8.1-so-that-you-can-install-unsigned-drivers/

1) Enter EDL mode. Some phones have multiple ways to get into EDL mode but there is one method that works universally.

1.1) Download and install fastboot and adb drivers from here.
https://drive.google.com/file/d/0B0MKgCbUM0itNVB1elljU2NPR0k/view
Answer "y" to all the questions. Install MiFlash as well if you haven't already, from here.
https://drive.google.com/open?id=0B3cbhaQTfWruQXY2N3JiVl80Y0E

1.2) Enable USB debugging in developer options (Settings > Additional settings > Developer options) on the phone. If you can't see developer options, go to about phone and start tapping the MIUI version until the phone says you are a developer.

1.3) Connect your phone to your PC and open a command prompt (Win+R, type in cmd). In command prompt, type in

adb devices
1.4) Your phone will ask for authorisation, allow it, then type in

adb reboot edl
1.5) If your phone says it's in download mode OR the screen is completely blank (the notification LED might be blinking), you're in EDL mode.

2) Open Device Manager in Windows. If the phone appears as a port by the name Qualcomm HS-USB QDLoader 9008, skip to step 3. In case it's recognised as QHSUSB_BULK or something else, proceed.

2.1) Right-click on it (QHSUSB_BULK) and choose to update driver. Choose to browse for driver.

2.2) Enter this location

C:\Program Files\Xiaomi\MiPhone\Qualcomm\Driver
and click next. Install the driver.

3) Proceed with the regular fastboot flashing instructions.

3.1) Download the fastboot ROM that you want to install from here.
http://en.miui.com/a-234.html

3.2) After the fastboot ROM finished downloading, unzip the archive.

3.3) Launch MiFlash and there browse for the root directory of the unzipped fastboot ROM (where flash_all.bat and other batch files are). Refresh in MiFlash. Your device will appear as a COM port.

3.4) Select flash all at the bottom of the window and click flash.

3.5) Wait until it says the device has been flashed successfully. Done.