Satellite imagery is formed by finite digital numbers representing a specific location of ground surface in which each matrix element is denominated as a picture element or pixel. The pixels represent the sensor measurements of spectral radiance. The radiance recorded in the satellite images is then an integrated sum of the radiances of all targets within the instantaneous field of view (IFOV) of the sensors. Therefore, the radiation detected is caused by a mixture of several different materials within the image pixels. For this reason, spectral unmixing has been used as a technique for analysing the mixture of components in remotely sensed images for almost 30 years. Different spectral unmixing approaches have been described in the literature. In recent years, many authors have proposed more complex models that permit obtaining a higher accuracy and use less computing time. Although the most widely used method consists of employing a single set of endmembers (typically three or four) on the whole image and using a constrained least squares method to perform the unmixing linearly, every different algorithm has its own merits and no single approach is optimal and applicable to all cases. Additionally, the number of applications using unmixing techniques is increasing. Spectral unmixing techniques are used mainly for providing information to monitor different natural resources (agricultural, forest, geological, etc.) and environmental problems (erosion, deforestation, plagues and disease, forest fires, etc.). This article is a comprehensive exploration of all of the major unmixing approaches and their applications.