Just to share my part. In our house we have had mice over the years. In terms of getting rid of them, we have tried many things, including live traps.
Right now we use this box that you buy, its black with two entrances. Inside their is a poison that does something to the mice. They search for water, and they become weak and slow. Our dog, the sausage dog or salsicha, hunts the mice. So when they are weak he usually gets them.
There are definitely some real concerns with having mice in the house, in how they could chew through electrical cables. Because I grew up with my mom, I simply went with whatever she decided, so I personally never observed this point for myself.