When I caught HPV it took three treatments for the warts to go away permanently. The first time was acid based, the following two times were via laser. It has now been about 8 years and I have not seen them again.
Although they say 25-50% of women have HpV(but not all strains show visible warts) my wife and I have two kids and she has never shown any symptoms. For a long time she was on the pill, but we have also used condoms over that time.
They say that you are never completely cured, but I think that is more a function of there is no definitive test to confirm it. They say the virus lives in the skin, but it's been a while and no recurrence...