We present a model for describing the visibility of a polyhedral terrain from a fixed viewpoint, based on a collection of nested horizons. We briefly introduce the concepts of mathematical and digital terrain models, and some background notions for visibility problems on terrains. Then, we define horizons on a polyhedral terrain, and introduce a visibility model, that we call the horizon map. We present a construction algorithm and a data structure for encoding the horizon map, and show how it can be used for solving point visibility queries with respect to a fixed viewpoint.