The FAA does not preempt California law insofar as it invalidates a waiver of an employee’s right to bring PAGA claims arising out of Labor Code violations that affected the plaintiff employee. However, the FAA does preempt California law (Iskanian v. CLS Transportation Los Angeles, LLC (2014) 59 Cal.4th 348 and progeny) insofar as it precludes waiver of the employee’s right to litigate PAGA claims that arise from violations affecting only other employees. The FAA does not exempt from arbitration claims brought by or against sovereign states, but it also does not forbid arbitration of claims by an agent for one or more principals, such as wrongful death actions or shareholder derivative suits. On the other hand, the FAA does prohibit states from requiring a party to an arbitration agreement to choose between foregoing arbitration and allowing the arbitration to proceed with respect to claims that the parties did not agree to arbitrate. In prohibiting waiver of the employee’s ability to bring PAGA claims arising from Labor Code violations that affect only other employees, California law forces such a choice and so is preempted to that extent.