Hyperspectral imaging is a process of spectral analysis with high resolution by recording hundreds of closely spaced, narrow bands, the presence of which allows the accurate determination of surface materials. The spectrum of the information is rich, making it useful in a wide range of applications, such as environmental monitoring, precision agriculture, geological exploration, and biomedical diagnostics. Hyperspectral image analysis relies on spectral unmixing, which breaks mixed pixels into spectral signatures of constituent (endmembers) and determines their quantities. These are very important processes in the area of classification, anomaly detection and change analysis. There are three broad areas of unmixing techniques: mixing model, algorithmic strategy and learning paradigm. The interaction of materials within a pixel is characterized as mixing models, from linear to nonlinear formulations. The algorithms include: geometric methods, statistical methods, and decomposition methods of spectral disentanglement. The paradigms of learning center on model generalization and they develop out of supervised models to deep learning models which take advantage of spectral-spatial dependencies. This literature review summarizes these methodologies, their development with respect to theoretical bases, and algorithm development. It points to the transition of models based on heuristics to data-focused models and the integration of learning algorithms and physical modeling. The major challenges: spectral variability, noise resilience, model interpretability will still be the topic of further research. The future trends are posing hybrid approaches that integrate the domain knowledge with the adaptive learning to increase the robustness and applicability in real world contexts.