I get calluses on the soles of my feet, that can become so thick that they become painful. I've been looking for a long time for something that would remove them properly (most of what I've tried has been quite useless). This certainly does the trick, but it is basically using a razor blade to shave off a layer of skin/callus, so you have to be careful about how much you shave off, so that you only take off the top layers of the callus and not go too deep or you leave the skin on the base of your foot too thin, which is just as painful to walk on as the original callus! Once you have mastered the technique (it's not hard, just hold the metal head flat against the base of your foot and draw it across the callused area firmly but not with too much pressure) anyone with problematic calluses will find it invaluable, I'm sure! I use it about once a month.
I don't get corns, but I believe they're fairly similar, so I'd imagine it's worth giving this a go on them too.