Nowadays, hyperspectral remote sensors are readily available for monitoring the Earth's surface with high spectral resolution. The high-dimensional nature of the data collected by such sensors not only increases computational complexity but also can degrade classification accuracy. To address this issue, dimensionality reduction (DR) has become an important aid to improving classifier efficiency on these images. The common approach to decreasing dimensionality is feature extraction by considering the intrinsic dimensionality (ID) of the data. A wide range of techniques for ID estimation (IDE) and DR for hyperspectral images have been presented in the literature. However, the most effective and optimum methods for IDE and DR have not been determined for hyperspectral sensors, and this causes ambiguity in selecting the appropriate techniques for processing hyperspectral images. In this letter, we discuss and compare ten IDE and six DR methods in order to investigate and compare their performance for the purpose of supervised hyperspectral image classification by using K-nearest neighbor (K-NN). Due to the nature of K-NN classifier that uses different distance metrics, a variety of distance metrics were used and compared in this procedure. This letter presents a review and comparative study of techniques used for IDE and DR and identifies the best methods for IDE and DR in the context of hyperspectral image analysis. The results clearly show the superiority of the hyperspectral signal subspace identification by minimum, second moment linear, and noise-whitened Harsanyi-Farrand-Chang estimators, also the principal component analysis and independent component analysis as DR techniques, and the norm L1 and Euclidean distance metrics to process hyperspectral imagery by using the K-NN classifier.