Mole control is not something that can be easily achieved. Both keeping moles out of your garden, or another plot of land, and getting rid of moles once they are there, is not easy. There are mole treatment techniques that you can try, and they should have at least some success, but it is unlikely to get rid of all of them.
It is almost as if the less people are bothered by something the harder it is to get rid of them. Wasps, for example, would surely take precedence over moles as a pest control problem. Say someone was dealing with both wasps and moles, but only one could be dealt with, surely every sane person would choose wasps. Wasps can hurt when they sting you, moles don't even come near you. Yes, moles can mess up your garden, but surely a messy garden is preferable to being stung. Of course with a wasps nest, being stung multiple times is a big fear as well. In any case, if you accept that, then you can see that it is far easier to get rid of wasps. One simple spray with a professional insecticide and they will soon all be dead.
Rats are another one that are horrible to have around and would take preference over moles in terms of which one you would get rid of first. They are dirty, spread diseases, and will bite you given half the chance. Again though, they're quite easy to get with traps and rat poison.
With moles though, yes there are traps but you're unlikely to get all of the moles. There's also poison in terms of gas, but again you probably won't get all of them. Perhaps this is more to do, however, with the fact that moles stay outside in the garden where it is harder to control them. Also they hide underground.
They are not good creatures to have around. They are incontinent, meaning that they wee everywhere. They also leave their faeces everywhere as well. You don't want to think about what could happen if a pet or a child found one of these and thought it was a raisin either. They can get up on counters, they can get into cupboards. They can chew through most things, in fact they are always chewing on things. You'll find your furniture chewed, your door frames, and just about anything else they can get their teeth around. Even wires, so they are quite a significant fire hazard as well.
You could try using natural pest control for them, for example by getting a cat. This is quite an elegant solution but is not always the most effective. Sometimes the cats just play with the mice and don't deal with them properly. Human pest controllers, on the other hand, tend to use mouse traps or mouse poison, which is more reliable.
If you want to deter mice from coming in the first place though you just have to keep your abode in pristine conditions. No food lying around. No faulty plumbing. You should be fine. You should do this once you find a mouse infestation as well to make sure it does not spread.