I got a planter wart on my foot after a lovely stay at a Disney resort--nice souvenir. Had the thing for over 2 years and finally asked my doctor to look at it when I had a physical. He told me this type of wart was caused by a virus and until the body decides to attack it, the wart won't fully go away. He said that by irritating the wart and the skin around it, the body can trigger itself to produce the things (antibodies?) to attack the virus. Then he prescribed a strong wart remover and duct tape. Yes, duct tape.
Well, months later that didn't work. I ended up having to go every week for 2 months and having the thing frozen and bathed in acid. It hurt. It also was considered "surgery" and cost my insurance company several thousand dollars. After the last treatment, I was fed up with the pain and decided to live with the stupid thing on my foot. After about a month, my body somehow rejected the wart and fought the virus. It just sort of disappeared.