Jail is a possibility so this is a criminal action, however it differs a bit in that the other party is often the prosecutor who brings charges against the other party and must prove 1) there was a valid unambiguous order, 2) person charged was present when the oral order was made or was properly served the written order, 3) had the ability to comply with the order, and 4) willfully violated the order.
Statute of limitations: for support payments 3 years from date each payment was due, for other orders 2 years.