At the US Federal level the law is "one party consent", meaning that someone who is a party to a private conversation can record it without requiring the approval of the other part(y/ies). You can't record someone else's private conversation without approval, but you can record those you are a party to.

Some states have stricter "two party consent" laws which require both/all parties to approve, which is why most national companies put automated warnings in their phone systems if they're recording any calls.