We study four dimensional N = 2 supersymmetric gauge theories with matter multiplets. For all such models for which the gauge group is SU(2), we derive the exact metric on the moduli space of quantum vacua and the exact spectrum of the stable massive states. A number of new physical phenomena occur, such as chiral symmetry breaking that is driven by the condensation of magnetic monopoles that carry global quantum numbers. For those cases in which conformal invariance is broken only by mass terms, the formalism automatically gives results that are invariant under electric-magnetic duality. In one instance, this duality is mixed in an interesting way with SO(8) triality.