Factors such as low spatial resolution and material heterogeneity result in the issue of mixed pixels in images, which makes pixel-level data processing and applications unable to meet the practical requirements. Spectral unmixing extracts information of endmembers and abundances at the sub-pixel level and offers technical support for fine quantitative analysis of data in real applications. This paper introduces research advances of spectral unmixing theories, methods, and applications in recent years. Technical research results include linear and nonlinear mixture models, and methods under the principle frameworks of geometry, regularized optimization, and statistical machine learning. Moreover, improvements provided by spectral unmixing for other techniques such as classification, and theoretical and practical values of spectral unmixing in handling problems from remote sensing to indoor applications such as medical science are analyzed. Finally, drawbacks in spectral unmixing technical and application researches and the necessity of their synergistic development are summarized.