Is it possible to view WebP images in nautilus / photo program?

There is a plugin for the GIMP, written by Nathan Osman.

You can add this plugin from his webptools PPA:

sudo apt-add-repository ppa:george-edison55/webp

Then install the required package: gimp-webp

sudo apt-get install gimp-webp

As for thumbnails in nautilus, this seems to be a bug with MIME, as apparently (so I was told) Nautilus already "supports" the webp format, but the thumbnails do not show up as they should.

Since 16.04

display image.webp

or for thumbnails

display 'vid:*.webp'

Imagemagick does support webp now, although it uses webp, so you need to install webp

sudo apt-get install webp

Since 14.04 [universe] there is the vwebp command in the webp package:

sudo apt install webp

Then:

vwebp imagefile.webp

To get thumbnails in Nautilus see this answer (like Aquarius Power said above).