"Libel" involves the publishing of a falsehood that harms someone. Slander is the same doctrine applied to the spoken word. Collectively, they are referred to as "defamation". Both are a matter of state laws, which usually (not always) require that the falsehood be intentional.
In New York Times v. Sullivan, the Supreme Court held that the First Amendment requires that, before a public official can recover damages for a defamatory statement, he must prove it was made with "actual malice", even if state laws otherwise allow recovery for negligent defamation. The Court has since expanded this to cover not only public officials but "public figures", including individuals who involve themselves in controversies.