Hyperspectral imaging uses a wide range of spectral bands with narrow and contiguous spans to capture and process information. The extensive spectral bands in hyperspectral images offer abundant spectral details for classification. Its ability to capture and analyze data across numerous narrow and contiguous spectral bands makes it especially suitable for applications in agriculture, environmental monitoring, mineral exploration, urban planning, water resource management, and more. Nevertheless, this increased dimensionality can pose challenges, including computational complexity and the existence of redundant information. The focus of this review lies in the fundamentals of hyperspectral imaging (HSI) and its dimensionality reduction methods especially feature extraction (FE) techniques. It covers FE techniques like knowledge-based, wavelet-based, statistical, deep learning, and clustering-based methods. Feature extraction is a critical preprocessing step that aids in reducing redundancy, diminishing dimensionality, and amplifying discriminative information. The process involves transforming the original data into a new space with dimensions that differ. This review provides a valuable foundation for future studies exploring dimensionality reduction techniques in hyperspectral image analysis.