Having moles shows that you have wonderfully fertile soil with lots of earthworms aerating it, pulling down leaves and compost and turning it into something your plants can use as feed. We have a few moles, whereas the farmer around us has none because he uses persistent wormers for his livestock. The wormers kill the earthworms, so the moles don't come as there's no food for them.
The downside of that is your soil will be far less fertile than when earthworms are present.
Every few years we get fed up with the molehills so we get the mole catcher in. He gets about 20 then stops (probably so he has to come back, keeping himself with a customer - or is that too cycnical?)
Mostly we tolerate the moles. The dogs catch them sometimes but make more mess doing so than the moles themselves do. Their spoil hills are great for new soil for the tunnel and garden, and we really miss that in molecatcher years.