We show that certain exactly marginal and relevant deformations of N=4 theory which preserve N=1 supersymmetry, exhibit rich infrared dynamics. These theories have moduli spaces with discrete (Higgs) branches. On certain branches the theory flows to the Klebanov-Witten conifold SCFT, while on other branches the theory undergoes a Seiberg duality cascade terminating in an N=1 theory with a mass gap. Using the matrix model approach the quantum moduli spaces and quantum superpotentials of these theories can be computed exactly. In the D-brane picture these quantum moduli spaces correspond to the Calabi-Yau space in the geometric dual description of the gauge theory.