This is a very timely question for a growing number of US dual-citizens and those in a position to be dual-citizens -- as many such persons resident beyond the US are getting into family/spousal conflicts and/or are being denied service because of things such at FATCA compliance or other US Treasury/IRS-related hassles (even when the IRS/US Treasury has been paid in full for the person's entire history of being subject to IRS/Treasury rules).

As a matter of practice for travel to/from the US, the outcomes in part depend on whether or not the person is born in the US. When it comes to VWP country citizens who were former U.S. citizens who happened to acquire US citizenship as a result of conditions applicable to them at their birth outside of the US, I've seen such persons apply for an ESTA and get in and out of the US under the VWP without any extraordinary peep from CBP. However, if place of birth is in the US, the chances of hassles during the trip and on US arrivals (and sometimes even US departures) skyrocket -- much the same goes also for those who were never US citizens but happened to be born in the US.