Hyperspectral imagery is widely used for the identification and monitoring of earth surface, which in turn need good classification performances. However, the high spectral dimensionality of hyperspectral images degrades classification accuracy and increases computational complexity. To overcome these issues, dimensionality reduction has become an essential preprocessing step in order to enhance classifiers performances using hyperspectral images. Dimensionality reduction tackles the problem of the high dimensionality, but also the high correlation between the spectral bands of hyperspectral images. In this paper, we first review the main dimensionality reduction approaches and compare their performances when used for the classification task using the Support Vector Machines classifier. We also propose a combination of feature extraction and band selection for classification. We report the performances of all these methods using real hyperspectral images and show their efficiency for hyperspectral image classification.