Laptop works fine with Mint starting from 18.2. With older Mints, wifi does not work yet since the Intel 8165 wifi adapter needs kernel >= 4.7. I did not need to install drivers for any hardware.
With 18.2, wifi, HDMI, sound and the webcam are all working fine, as well as the SSD which uses the NVMe protocol (tested with the 512GB model, which is actually a Samsung M.2 SSD). Lenovo's ethernet adapter and USB-C to VGA adapters work without any problem. I have not tested any other USB-C devices.
Keyboard backlight can be controlled by the usual Fn-Space, and also by the Cinnamon power applet.
|What doesn't work:|
The fingerprint reader.
The LED of the microphone on/off button is not working.
The Bluetooth function key does not work yet, but is reported to work on Linux kernels >= 4.12. I have not yet tested this.
|What was done to make it work:|
I had to do partitioning manually to be able to install Mint. The Windows disk was originally encrypted with Bitlocker; to dual-boot, I disabled the Bitlocker encryption which turned the C: disk into a normal NTFS partition, allowing it to be resized with GParted. I manually added a root (ext4) and swap partition, then went to install Mint putting the bootloader on the "Windows Boot Manager" partition. This way dual-boot works fine, Mint and Windows can be loaded from Grub.
To make trackpoint scrolling work, I installed xserver-xorg-input-libinput from the repository, and then created a file .xinitrc in my home directory with:
xinput set-prop "PS/2 Generic Mouse" "libinput Scroll Method Enabled" 0 0 1
After making this file executable, logging out & in again was sufficient to make trackpoint scrolling working.
Note that there are reports of other X1 Carbon models where the trackpoint has a different name than "PS/2 Generic Mouse". Check the name of the mouse in terminal using: xinput
Tested with: Model 20HRCT01WW (i5 CPU, 8GB RAM, 512GB SSD, FHD display)