In this paper, we present a model based on a collection of nested horizons to describe the visibility of a terrain with respect to a viewpoint. We introduce first a formalization of mathematical and digital terrain models, and some background notions for visibility problems on terrains. Then, we define horizons and shadows on a polyhedral terrain, and introduce a few horizon-based visibility maps of a terrain. Finally, we present two algorithms for building the nested horizons on a polyhedral terrain. An application to the solution of point-to-point visibility queries are briefly discussed.