The WebP image format has been around for about five years, but till recently it’s been mostly a curiosity. I last blogged about it in 2013, when it didn’t have very wide support. Since then most browsers have adopted it, and now Google+ is making more use of it (no surprise, since Google is the format’s principal backer). It promises smarter lossy compression than JPEG and smaller file sizes for the same image quality.
The details of compression algorithms are beyond my expertise, but the article “A New Image Format for the Web”, from the Google developer site, offers a good high-level technical introduction.
A big problem is a lack of support by image editing software. Photoshop and GIMP both require a third-party WebP plugin. Until image editors support WebP out of the box, it’s going to be at a disadvantage. Recent statistics from W3Techs don’t show WebP at all, even in the “less than 0.1%” category.
Mad File Format Science 
It’s only really Opera and the Chrome-based browsers AFAICT – http://caniuse.com/webp
You may be right. I’ve seen a chart claiming broader support (can’t remember where now) but it might have been unduly optimistic.
Here’s a WebP gallery for testing. In Firefox and Safari, I’m seeing just placeholders for the WebP images.