Phase transitions can often be linked to the spectral properties of certain physical operators. In the theory of the strong interactions the fundamental breaking of chiral symmetry is intimately linked to the spectrum of the Dirac operator. When, however, quarks are favored over anti quarks by means of a chemical potential the Dirac operator becomes non hermitian. In this case the link between the Dirac spectrum and breaking of chiral symmetry has remained a puzzle (The Silver Blaze Problem) for more than two decades. In this talk we discuss how Random Matrix Theory solves this problem.