  In this paper, we study the birational geometry of the Hilbert scheme of n
points on P^2. We discuss the stable base locus decomposition of the effective
cone and the corresponding birational models. We give modular interpretations
to the models in terms of moduli spaces of Bridgeland semi-stable objects. We
construct these moduli spaces as moduli spaces of quiver representations using
G.I.T. and thus show that they are projective. There is a precise
correspondence between wall-crossings in the Bridgeland stability manifold and
wall-crossings between Mori cones. For n at most 9, we explicitly determine the
walls in both interpretations and describe the corresponding flips and
divisorial contractions.
