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Digital elevation models (DEMs) are widely used in geoscience. The quality of a DEM is a primary requirement for many applications and is affected during the different processing steps, from the collection of elevations to the interpolation implemented for resampling, and it is locally influenced by the landcover and the terrain slope. The quality must meet the user’s requirements, which only make sense if the nominal terrain and the relevant resolution have been explicitly specified. The aim of this article is to review the main quality assessment methods, which may be separated into two approaches, namely, with or without reference data, called external and internal quality assessment, respectively. The errors and artifacts are described. The methods to detect and quantify them are reviewed and discussed. Different product levels are considered, i.e., from point cloud to grid surface model and to derived topographic features, as well as the case of global DEMs. Finally, the issue of DEM quality is considered from the producer and user perspectives.