Terrains are a crucial component of three-dimensional scenes and are present in many Computer Graphics applications. Terrain modeling methods focus on capturing landforms in all their intricate detail, including eroded valleys arising from the interplay of varied phenomena, dendritic mountain ranges, and complex river networks. Set against this visual complexity is the need for user control over terrain features, without which designers are unable to adequately express their artistic intent. This article provides an overview of current terrain modeling and authoring techniques, organized according to three categories: procedural modeling, physically-based simulation of erosion and land formation processes, and example-based methods driven by scanned terrain data. We compare and contrast these techniques according to several criteria, specifically: the variety of achievable landforms; realism from both a perceptual and geomorphological perspective; issues of scale in terms of terrain extent and sampling precision; the different interaction metaphors and attendant forms of user-control, and computation and memory performance. We conclude with an in-depth discussion of possible research directions and outstanding technical and scientific challenges.