WebP image files are becoming more and more common on the web. Eye of GNOME (eog) doesn't support it out-of-the-box. Some browsers do, and ImageMagick as well by just installing the webp package (magick/convert -list format).
A simple search leads to webp-pixbuf-loader, but might be not that easy for beginners to find and follow that instructions.
How can I add WebP support to Eye of GNOME?
References
Old issue on Bugzilla: Bug 700751 – Support of images in format "WebP" in EOG.
Newer issue on GitLab: Cannot open WebP file.
eog uses GDK-PixBuf, which does not provide support for most formats itself (due to maintainability), but instead has support for formats added by the libraries that actually implement the image format. Currently libwebp, the library in question, does not provide any loader for GDK-PixBuf, but the linked repository (https://github.com/aruiz/webp-pixbuf-loader) provides one.
Downstream on Launchpad on gdk-pixbuf (duplicated on libwebp) and eog.
On Debian