Without use of imaging spectrometry, imaging of the Earth's surface from aircraft and from spacecraft is hampered by the low spectral resolution and limited number of spectral bands, typically less than 10 bands of 100 to 200 nm width. Imaging spectrometry in remote sensing concerns the acquisition of image data in many narrow (< 40 nm wide) contiguous spectral bands with the ultimate goal of producing detailed spectral reflectance curves for each pixel in the image. Many minerals and rocks have unique spectral signatures with characteristic absorption features that are 20 to 40 nm wide. Imaging spectrometers allow to depict these narrow features and thus map surface mineralogy based on spectral image characterization. This paper gives a review of imaging spectrometry and addresses the following topics: airborne and spaceborne systems available, spectral and geometric data pre-processing, atmospheric correction, techniques for thematic data analysis, and applications in the field of geological remote sensing. In the final section a case study is described where imaging spectrometer data is used for mapping surface mineralogy in a hydrothermal alteration system, thus guiding gold exploration.