Abstract Starting from a concept of the land surface, its definition and subdivision from Digital Elevation Models (DEMs) is considered. High-resolution DEMs from active remote sensing form a new basis for geomorphological work, which is moving on from consideration of whether data are accurate enough to how the surface of interest can be defined from an overabundance of data. Discussion of the operational definition and delimitation of specific landforms of varying degrees of difficulty, from craters to mountains, is followed by the applicability of ‘fuzzy’ boundaries. Scaling, usually allometric, is shown to be compatible with the scale-specificity of many landforms: this is exemplified by glacial cirques and drumlins. Classification of a whole land surface is more difficult than extraction of specific landforms from it. Well-dissected fluvial landscapes pose great challenges for areal analyses. These are tackled by the delimitation of homogeneous elementary forms and/or land elements in which slope position is considered. The boundaries are mainly breaks in gradient or aspect, but may also be in some type of curvature: breaks in altitude are rare. Elementary forms or land elements are grouped together into functional regions (landforms) such as ‘hill sheds’. It may often be useful to recognise fuzziness of membership, or core and periphery of a surface object. Plains and etched or scoured surfaces defy most of these approaches, and general geomorphometry remains the most widely applicable technique. It has been applied mainly within arbitrary areas, and to some extent to drainage basins, but more experimentation with mountain ranges and other landforms or landform regions is needed. Geomorphological mapping is becoming more specialised, and its legends are being simplified. Its incorporation into geographical information systems (GIS) has required greater precision with definitions, and the separation of thematic layers, so that it is converging with specific geomorphometry and becoming more flexible and more applicable, with a broader range of visualisation techniques.