Copyright law for cover songs

Whenever you use or record a cover of an existing song, you are using someone else’s copyrighted material.
That being said, cover songs can be perfectly legal, even encouraged (at least in most countries, including:

When a version or derivative of the copyrighted song is created, it is referred to as a cover.
A cover song needs to get permission, or a license, from the copyright holders in order to record it or use it in any way.
Once you create a licensed cover and record it, it is now copyrighted and you can register your copyright.