The League of Legends, Institute of War

Can someone explain to me exactly where the League stands at the moment? From my understand the League was created as a result from the destruction caused by the Rune Wars. They are a group dedicated to preventing wars like that again. Ok sure; they gather strong fighters of various nations to enforce their political rule. They also takes various heads of each nation to represent their nation in the League. So basically early America... What confuses me is: Is there war on Runeterra at this very moment? If the League is created and governed by Demacia and Noxus do the Demacians and Noxian's get along?