I tried looking at the tutorials and docs, but didn't immediately find any mention of images. Does it do images in a sane way, or does it require third-party plugins?
It doesn't. In fact it doesn't do anything for assets in general. But integrating it with Webpack is quite straightforward if you're comfortable with Webpack.
Ok. I saw all those "make a blog with Eleventy" examples but an integral part of a blog is images and of course automatic resizing of preview etc of those.