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.