Hyperspectral images usually contain hundreds of contiguous spectral bands, which can precisely discriminate the various spectrally similar classes. However, such high-dimensional data also contain highly correlated and irrelevant information, leading to the curse of dimensionality (also called the Hughes phenomenon). It is necessary to reduce these bands before further analysis, such as land cover classification and target detection. Band selection is an effective way to reduce the size of hyperspectral data and to overcome the curse of the dimensionality problem in ground object classification. Focusing on the classification task, this article provides an extensive and comprehensive survey on band selection techniques describing the categorisation of methods, methodology used, different searching approaches and various technical difficulties, as well as their performances. Our purpose is to highlight the progress attained in band selection techniques for hyperspectral image classification and to identify possible avenues for future work, in order to achieve better performance in real-time operation.