Nowadays you can buy small network attached boxes to function as small home-office disk servers so cheaply, that most of the time I take backups by having a couple of those lying around the house. But for many years I used to backup my personal Linux desktop by burning CD's and then DVD's.
The challenge with backing up to a CD/DVD is that you easily have more data to back up than fits on one disc. The TAR utility was created for tapes and completely lacks any capability of splitting itself into parts. What's more, with TAR you create the archive first, and then compress it, so it is not possible to know in the TAR phase when you've actually reached the size of your CD or DVD, and in the compression phase it is generally too late.