Tattoos do the job without the problems.

Registered id tags and microchips do a good job at getting pets back home to their family. They both have drawbacks though.
Id tags on an animal's collar can be lost if the animal pulls out of the collar or thrown away by someone who would rather keep your pet than return it.
Microchips have more problems some of them life threatening. They have been known to migrate from its proper placement between the shoulder blades. This makes them less effective as a rehoming tool. Several companies make microchips with differing technologies. Scanners only read for the chips made by that company. Most animal shelters are strapped for money and can't afford to by several scanners. A life threatening problem with microchips is their link to sarcomas (cancer).
Tattoos are permanant. Once placed they cannot be removed nor will they move out of place. They are visable, no expensive scanner is needed. At most a pair of clippers is needed to keep the hair trimmed short in the area of the tattoo making it easier to see.
Tattoos have been used for eons on humans and animals as decoration and for identification. Never has there been a link to cancer. The closest has been a tattoo being placed over a mole making it harder to observe for changes in appearance.
None of the identification techniques work unless their is a readily available system to track the animal back to the owner. If you use any of these systems it is imperative to have it registered with a national registry.