Organic Fungus Nuker
A blister forms and eventually sloughs off, taking the wart with it. The liquid nitrogen freeze is more likely to be effective than over-the-counter freezing options, simply because it's so darn cold. This method can be painful, so take care before treating children with cryotherapy.
Cantharidin - Another way to kill the tissue in the wart is by applying a substance produced by the blister beetle. You may get an uncomfortable blister from this method, but the application of cantharidin itself isn't likely to be painful.