Does anyone know how it works if you live on one side of the border of a state and work in the other?

What state gets your taxes? Do you pay in both?
In the future I want to move to the border of N.C. but we may have to find employment in VA. Since we want to go to a small town that will probably not have many job opportunities locally but will have cheaper homes to purchase, I was wondering if it would be worth it.