I will introduce a parabolic flow of Hermitian metrics which is a generalization of Kähler-Ricci flow. This flow preserves the pluriclosed condition, and its existence and convergence properties are closely related to the underlying topology of the given complex manifold. I will discuss a stability result for the flow near Kähler-Einstein metrics. Further, I will classify static solutions to the flow on various classes of complex surfaces, and show that no static solutions exist on Class VII surfaces. Finally I will discuss possible applications of this flow to understanding the topology of nonKahler surfaces. Joint with G. Tian.