Appears in collection : Jean-Morlet Chair : School on geometry and dynamics / Chaire Jean-Morlet : Géométrie et systèmes dynamiques

I will present results on the dynamics of horocyclic flows on the unit tangent bundle of hyperbolic surfaces, density and equidistribution properties in particular. I will focus on infinite volume hyperbolic surfaces. My aim is to show how these properties are related to dynamical properties of geodesic flows, as product structure, ergodicity, mixing, ...