A few days ago I found out that Dell had released a new version for my XPS13 (9360) BIOS.

Here are the steps I followed to update the BIOS (no USB key or wine or Windows boot required \o/).

Dell has a page that explains some of it.

Check BIOS version

First, check out your BIOS version:

$ sudo dmidecode -s bios-version
[sudo] password for etienne:
1.3.5

Check latest BIOS version available online

Compare the result (1.3.5 here) with the version stated by Dell either on the Dell website directly (look for 'BIOS' category) or on this website.

If your BIOS is not up-to-date, download the latest BIOS (a .exe file named something like XPS_9360_2.1.0.exe) from the Dell website.

Copy the BIOS file to the EFI folder

Copy this file to your /boot/efi folder

$ sudo cp ~/Downloads/XPS_930_2.1.0.exe /boot/efi

Update the BIOS with BIOS Flash Update

Reboot your XPS13 and push the F12 key during boot to start the Dell boot menu.

In the boot menu, choose "BIOS Flash Update":

BIOS Flash Update

A popup will open and you will be able to select the correct BIOS file (the one you just downloaded and copied to /boot/efi):

BIOS file selection

Click on Begin Flash Update and the new BIOS starts to update (it will only start if the power supply is plugged in):

BIOS Update in progress

After a few minutes the computer reboots with the new BIOS!

$ sudo dmidecode -s bios-version
[sudo] password for etienne:
2.1.0

Sources: this, this, this.