How does Titanium Backup work? When will it not work? How does it know what to back up? Can an app have data that TB won't know about or that TB won't back up?

Other than restoring a Jellybean backup to a Gingerbread phone, how else will Titanium Backup fail to restore apps or will destabilize my phone?

I need to be sure I don't lose data as I reset ROMs or phones or switch between two ROMs or phones.
I advise you to read thoroughly the following resources before taking any step to make changes to your OS, so you can be sure if you're doing things right with Titanium Backup:


Titanium Backup User’s Guide: The Titanium Backup manual.
Titanium Backup Technical FAQ: The most frequently asked questions.
Titanium Backup Troubleshooting: In case you have problems…
Titanium Backup Cryptography: All about encrypting and decrypting your backups.
Titanium Backup Tips &amp; Suggestions: Some useful tips.
Titanium Backup HOWTOs: This can help you get some specific jobs done.
Titanium Backup Licensing: If you have questions or problems with license keys for the Donate version or the PRO version on the Market.