What is the WebP Image Format (And Why Does It Matter)?

I must admit, this format is a new one on me. But I do think the web needs another image format that uses lossy compression and supports alpha.
PNG is a great format for the web, but not is all cases. On images with a lot of flat colour, like logos, graphics, charts, cell-shaded cartoons, png offers very efficient compression, with the flawless quality of being lossless and the added bonus of an alpha channel. That makes it good for things like logos and icons. Though svg is rightly taking over in these cases.
But where png falls down is images with more detail and variation in colour and tone, such as photos, paintings, CGI renders, etc… The lossless compression is less efficient then. Of course we normally just use a good old jpeg for photos and suchlike, but when you want alpha on one of these type of images, jpeg is not an option, and the png can end up with a file larger than we would like on the web.
For this reason I would welcome a new format that offers jpeg-like lossy compression and alpha at the same time. I’ve not tried webP yet to see how it performs, so can’t say if it’s what I’m looking for. But the big thing putting me off is the lack of support in browsers. It looks like a no-go in IE, Firefox and Safari, which is a shame.