Appears in collection : Complex Geometry, Complex Analysis and Dynamics / Géométrie Complexe, Analyse et Dynamique Complexe

We will overview notions of conformal measures and currents, and a Patterson-Sullivan method of constructing them, in various branches of Holomorphic Dynamics: for 1D rational maps and their natural extensions, complex Henon maps and classical Kleinian group, with an eye towards an extension to higher rank actions.