Warts are a fickle ailment. At least one small but well designed study, done by real dermatologists showed some benefit to duct tape.....which is pretty close to what all other studies have shown regarding all other wart remedies including freezing with liquid nitrogen, lasers, topical immune modulators, etc etc. Bottom line is, alot of things work so-so, nothing works well and in the end, most warts eventually go away on their own....but it can take many many years....I still have a plantar wart from childhood.
By the way, the warts on the bottom of the foot are 'plantar' warts, not planter's warts which is what most people call them. 'Plantar' is just an anatomical term that refers to the bottom of the foot. So a plantar wart is mostly just and indication of where it is. The vast majority of warts, including plantar warts are the same thing, the medical term for which is verucca vulgaris....lovely name for a lovely problem.
They are caused by a virus and they are contagious, but not wildly contagious. But, if you scratch one, and then scratch some where else, then you can get additional warts. A lot of dermatologist wear gloves if they touch them....but then they get to touch a lot of warts.
In some cultures, specifically Carribean and possibly Appalachian, a witch doctor or healer would 'talk' the warts away. Since many warts spontaneously resolve on their own "talking" them off was probably as effective as any other method.
As Rox mentioned, the key is the immune system. Most methods that work mostly just irritate the wart causing inflammation. The inflammatory response triggers an 'immune response' that destroys the wart. Freezing, lasers, gels, duct tape, etc do not 'kill' the wart or the virus....your body does, it just needs that inflammation to jump start things.