Legality of online background checks to screen job candidates?

I was wondering what the rules are for investigating the backgrounds of job applicants.

Are you allowed to use online background check services? can you look into their credit history? is there a way to verify their past employers through their tax records? Criminal backgrounds?

Are these rules national? or is it a state-by-state thing. I’m mostly interested in the US, but I’d be interested to hear how other countries deal with this too. Thanks.