Yes, they can be cured, but most often people would get them treated without realizing that most of the treatments offer short term measures only, as they don't cure the problem.
The practice most often followed by doctors to rid you of warts is rather unbearably painful.
Often, the treatment lies in applying lengthy cotton swab that is dipped in dry ice till the latter is absorbed by cotton swab that is firmly pressed on to the wart.
It causes a burning sensation and drives the bearer crazy.
After a couple of days the wart falls off.
You bear the pain and seem to have gotten rid of the warts, but unfortunately the wart has a tendency to reappear in a matter of days, sometimes as early as a fortnight! The idea is not to discourage you from visiting a medico, but to inform you that there are other many other ways to treat warts and get rid of them forever.
Getting rid of warts forever doesn't mean having them removed for cosmetic effects only; it involves treatment of your skin in such a fashion that it prevents their growth forever.
Successful wart cures would generally entail quite a few ingredients including aloe Vera and salicylic acid.
These are potent constituents that rid you of warts for good by treating the root cause of the problem and not merely the symptoms.