In this paper we present the ongoing research on connection between digraphs associated to finite (commutative) rings and quiver representations. Digraph associated to a finite ring A has the set of vertices V = A2 and arrows (or edges) E = x, y → x + y, xy , x, y ∈ A . In another terminology, it is a finite quiver with loops. In addition to previous work to understand these graphs, the main goal of the present work is to introduce some new cohomological and quiver methods. These methods should provide us with better understanding of properties and classification of finite rings.