Please be aware that JAI is no longer actively developed or even maintained for years now. If you run into trouble, it won't ever get fixed. That may also be the reason why your internet searches (which you did do right?) are not turning up so much, I wouldn't use this API myself anymore given its zombie status.
I did find this when searching for "jai tutorial":
Applications? Perhaps you mean APIs or frameworks.
Not really anything to replace JAI, unless you want basic access to pixels - then the ImageIO and BufferedImage classes built into the JDK are enough. For anything else it will depend on what you want to do. JavaCV seems promising:
For anything else, do a search for "java jai alternative". That's how I got to this link at least.