We will explain the notion of T-duality in supergravity backgrounds with non-Abelian isometries and non-vanishing RR fluxes. We will then focus on type-II backgrounds on which the duality action preserves supersymmetry. For the case of D3-branes at the tip of the conifold dualising along an SU(2) isometry provides a type-IIA background with M-theory lift is of the type describing duals to certain N=1 SCFT quivers produced by M5-branes wrapping a Riemann surface. In the non-conformal cases we find smooth duals in massive IIA supergravity with a Romans mass naturally quantised. We initiate the interpretation of these geometries in the context of the AdS/CFT correspondence and discuss the fate of various charges under dualisation. The backgrounds suggest a form of Seiberg duality in the dual field theories which also exhibit domain walls and confinement in the infrared.