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Variable illumination and environmental, atmospheric, and temporal conditions cause the measured spectral signature for a material to vary within hyperspectral imagery. By ignoring these variations, errors are introduced and propagated throughout hyperspectral image analysis. To develop accurate spectral unmixing and endmember estimation methods, a number of approaches that account for spectral variability have been developed. This article motivates and provides a review for methods that account for spectral variability during hyperspectral unmixing and endmember estimation and a discussion on topics for future work in this area.