Image classification is one of the most basic operations of digital image processing. The present review focuses on the strengths and weaknesses of traditional pixel-based classification (PBC) and the advances of object-oriented classification (OOC) algorithms employed for the extraction of information from remotely sensed satellite imageries. The state-of-the-art classifiers are reviewed for their potential usage in urban remote sensing (RS), with a special focus on cryospheric applications. Generally, classifiers for information extraction can be divided into three catalogues: 1) based on the type of learning (supervised and unsupervised), 2) based on assumptions on data distribution (parametric and non-parametric) and, 3) based on the number of outputs for each spatial unit (hard and soft). The classification methods are broadly based on the PBC or the OOC approaches. Both methods have their own advantages and disadvantages depending upon their area of application and most importantly the RS datasets that are used for information extraction. Classification algorithms are variedly explored in the cryosphere for extracting geospatial information for various logistic and scientific applications, such as to understand temporal changes in geographical phenomena. Information extraction in cryospheric regions is challenging, accounting to the very similar and conflicting spectral responses of the features present in the region. The spectral responses of snow and ice, water, and blue ice, rock and shadow are a big challenge for the pixel-based classifiers. Thus, in such cases, OOC approach is superior for extracting information from the cryospheric regions. Also, ensemble classifiers and customized spectral index ratios S. D. Jawak et al. 178 (CSIR) proved extremely good approaches for information extraction from cryospheric regions. The present review would be beneficial for developing new classifiers in the cryospheric environment for better understanding of spatial-temporal changes over long time scales.