Hyperspectral unmixing involves estimating endmembers (pure materials) and their abundances in a scene from mixed spectral data. Hyperspectral cameras (HSCs) capture high-resolution spectral data, but due to low spatial resolution and multiple scattering, the measured spectra are mixtures of materials. Unmixing aims to decompose these mixtures into their constituent parts. This paper reviews unmixing methods from Keshava and Mustard's tutorial to the present, covering linear and nonlinear mixing models, signal-subspace, geometrical, statistical, and sparse regression-based approaches. Linear mixing assumes materials are macroscopically mixed, while nonlinear mixing involves interactions between materials. Unmixing is a challenging inverse problem due to model inaccuracies, noise, and environmental factors. Researchers have developed various models to address these challenges, including geometrical, statistical, and sparse regression methods. The paper discusses the linear spectral mixture model, signal subspace identification, and geometrical-based approaches like N-FINDR and VCA. It also covers statistical and sparse regression methods, emphasizing their use in unmixing. The paper concludes with a summary of the state of the art in hyperspectral unmixing and potential future developments.Hyperspectral unmixing involves estimating endmembers (pure materials) and their abundances in a scene from mixed spectral data. Hyperspectral cameras (HSCs) capture high-resolution spectral data, but due to low spatial resolution and multiple scattering, the measured spectra are mixtures of materials. Unmixing aims to decompose these mixtures into their constituent parts. This paper reviews unmixing methods from Keshava and Mustard's tutorial to the present, covering linear and nonlinear mixing models, signal-subspace, geometrical, statistical, and sparse regression-based approaches. Linear mixing assumes materials are macroscopically mixed, while nonlinear mixing involves interactions between materials. Unmixing is a challenging inverse problem due to model inaccuracies, noise, and environmental factors. Researchers have developed various models to address these challenges, including geometrical, statistical, and sparse regression methods. The paper discusses the linear spectral mixture model, signal subspace identification, and geometrical-based approaches like N-FINDR and VCA. It also covers statistical and sparse regression methods, emphasizing their use in unmixing. The paper concludes with a summary of the state of the art in hyperspectral unmixing and potential future developments.