Airborne and spaceborne hyperspectral imaging systems have advanced in recent years in terms of spectral and spatial resolution, which makes data sets produced by them a valuable source for land-cover classification. The availability of hyper-spectral data with fine spatial resolution has revolutionized hyperspectral image classification techniques by taking advantage of both spectral and spatial information in a single classification framework. The ECHO (Extraction and Classification of Homogeneous Objects) classifier, which was proposed in 1976, might be the first spectral-spatial classification approach of its kind in the remote sensing community. Since then and especially in the latest years, increasing attention has been dedicated to developing sophisticated spectral-spatial classification methods. There is now a rich literature on this particular topic in the remote sensing community, composing of several fast-growing branches. In this paper, the latest advances in spectral-spatial classification of hyperspectral data are critically reviewed. More than 25 approaches based on mathematical morphology, Markov random fields, segmentation, sparse representation, and deep learning are addressed with an emphasis on discussing their methodological foundations. Examples of experimental results on three benchmark hyperspectral data sets, including both well-known long-used data and a recent data set resulting from an international contest, are also presented. Moreover, the utilized training and test sets for the aforementioned data sets as well as several codes and libraries are also shared online with the community.