AVIF and WebP, two modern replacements for both JPEG and GIF on the web, both support lossy and lossless encoding.

WebP is mature and has more browser support, but AVIF is getting there (notably only lacking Edge support). Both can compress in either a lossy JPEG-like fashion or in a lossless PNG-like fashion.

If you use a image CDN like Imgix, it'll just auto-detect and serve whatever the most optimal format is anyway: https://docs.imgix.com/apis/rendering/auto/auto#format. Cloudinary too: https://cloudinary.com/documentation/image_optimization#how_...

For non-web, there's also JPEG XL to look at, but if you're not doing rendering an image for redistribution, it's probably better to keep it as raw as possible anyway (i.e. camera raw images plus photoshop layers, or whatever).