Morphological attribute profiles (APs) are among the most prominent methods for the spatial-spectral pixel analysis of remote sensing images. ince their introduction a decade ago to tackle land-cover classification, many studies have been contributed to the state-of-the-art, focusing not only on their application to a wider range of tasks, but on their performance improvement and extension to more complex earth observation data as well. Despite the overwhelming proliferation of deep learning-based methods in the past five years, APs are far from obsolete, due mainly to their high flexibility, low computational cost, lower training data requirement, and rigorous mathematical foundation. In this survey, an entire decade of more than 100 AP related contributions to the field of remote sensing have been compiled, providing an extensive panorama of this robust and effective tool. Moreover, a collective experimental comparison of the reviewed AP variations is provided as well, not only in terms of classification performance, but for the first time in terms of their generalization capacity too.