Given a directed graph (quiver) and an association of a natural number to each vertex, one can construct a representation of a Lie group on a vector space. If the underlying, undirected graph of the quiver is a Dynkin graph of A-, D-, or E-type then the action has finitely many orbits. The equivariant fundamental classes of the orbit closures are a key object of study. These fundamental classes are polynomials in universal Chern classes of a classifying space so they are referred to as "quiver polynomials." It has been shown by A. Buch that these polynomials can be expressed in terms of Schur- type functions. Buch further conjectures that in this expression the coefficients are non-negative. This talk will introduce some of the ideas behind the study of quiver polynomials, construct an example of a quiver polynomial using R. Rimanyi's iterated residue method, and discuss some of the quiver polynomials known to satisfy Buch´s conjecture.