Their success is their prolific rate of reproduction, like any other rodent species member. I've been shooting them for years in my suburban area, over 500 in the last 3 seasons. They have finally slowed down a bit, but they will continue to backfill. They have no natural predators left in the suburbs, and as another member mentioned, many more people feed them and think they are cute, than hunt them and do pest control. Here in VA they have a minimum of two broods a year (I think with warmer winter weather, they get in three), with 2-6 pups per brood.
I think the UK is a good example of how their population just cannot be checked no matter what they do. 7-10 M I think they are up to? Open year round hunting, no season. Trapping, Poison, etc. and they are not only not under control, they continue to proliferate.