Feature extraction plays a pivotal role in processing remote sensing datasets, especially in the realm of fully polarimetric data. This review investigates a variety of polarimetric decomposition techniques aimed at extracting comprehensive information from polarimetric imagery. These techniques are categorized as coherent and non-coherent methods, depending on their assumptions about the distribution of information among polarimetric cells. The review explores well-established and innovative approaches in polarimetric decomposition within both categories. It begins with a thorough examination of the foundational Pauli decomposition, a key algorithm in this field. Within the coherent category, the Cameron target decomposition is extensively explored, shedding light on its underlying principles. Transitioning to the non-coherent domain, the review investigates the Freeman–Durden decomposition and its extension, the Yamaguchi’s approach. Additionally, the widely recognized eigenvector–eigenvalue decomposition introduced by Cloude and Pottier is scrutinized. Furthermore, each method undergoes experimental testing on the benchmark dataset of the broader Vancouver area, offering a robust analysis of their efficacy. The primary objective of this review is to systematically present well-established polarimetric decomposition algorithms, elucidating the underlying mathematical foundations of each. The aim is to facilitate a profound understanding of these approaches, coupled with insights into potential combinations for diverse applications.