By turning up the earth, moles expose sheep to ingesting soil and this in turn can lead to listeriosis. Also, if there are moles in the lambing field, for some reason ewes are irresistably drawn to dumping their newborn lambs onto the hills. So you have a filthy muddy lamb, which even its mum doesn't want to lick. A very heavily pregnant ewe can, especially on a slope, roll over a molehill and be left stuck and unable to get up - here 'cowped'.
It's surprising how few moles it takes to cause a whole lot of hills.
If you have a shotgun, one way to get them is to creep up to the freshest molehill. Wait until you see the soil moving then fire straight down the hole.
Dogs can dig them out if they have patience and can wait until the mole is just about at the surface.
If you're going to use mole traps, make sure you rub them in soil and leave them to age for a bit before using them. Then don't handle them with your hands, as moles have an excellent sense of smell. The man who showed us how to do it, always wore the same manky old pair of rubber gloves to handle the traps and to lift out the dead moles. Don't forget to mark where you've buried the traps.