Abstract: An Einstein homogenous space is a smooth manifold G/H and with ricci curvature ric(x,y) = cg(x,y) where g(.,.) is the metric on G/H. An open question persists concerning the possible quotients, H, of noncompact Einstein homogenous spaces. Regarding this question, the Alekseevski conjecture states that H must be maximal compact. With this question and conjecture in mind, this talk will explore some of the things that are known about Einstein homogenous spaces and will present an approach for determining which Lie group quotients are NOT Einstein. Moreover, this talk will explore a tenable trajectory one could take in the quest of determining which G/H are not Einstein.