Recent drastic reductions in the Arctic sea-ice cover have raised an interest in understanding the role of sea ice in the global system as well as pointed out a need to understand the physical processes that lead to such changes. Satellite remote-sensing data provide important information about remote ice areas, and Synthetic Aperture Radar (SAR) data have the advantages of penetration of the omnipresent cloud cover and of high spatial resolution. A challenge addressed in this paper is how to extract information on sea-ice types and sea-ice processes from SAR data. We introduce, validate and apply geostatistical and statistical approaches to automated classification of sea ice from SAR data, to be used as individual tools for mapping sea-ice properties and provinces or in combination. A key concept of the geostatistical classification method is the analysis of spatial surface structures and their anisotropies, more generally, of spatial surface roughness, at variable, intermediate-sized scales. The geostatistical approach utilizes vario parameters extracted from directional vario functions, the parameters can be mapped or combined into feature vectors for classification. The method is flexible with respect to window sizes and parameter types and detects anisotropies. In two applications to RADARSAT and ERS-2 SAR data from the area near Point Barrow, Alaska, it is demonstrated that vario-parameter maps may be utilized to distinguish regions of different sea-ice characteristics in the Beaufort Sea, the Chukchi Sea and in Elson Lagoon. In a third and a fourth case study the analysis is taken further by utilizing multi-parameter feature vectors as inputs for unsupervised and supervised statistical classification. Field measurements and high-resolution aerial observations serve as basis for validation of the geostatistical-statistical classification methods. A combination of supervised classification and vario-parameter mapping yields best results, correctly identifying several sea-ice provinces in the shore-fast ice and the pack ice. Notably, sea ice does not have to be static to be classifiable with respect to spatial structures. In consequence, the geostatistical-statistical classification may be applied to detect changes in ice dynamics, kinematics or environmental changes, such as increased melt ponding, increased snowfall or changes in the equilibrium line.