Hyperspectral imaging acquires precise spectral information about the scene radiance that is exploited from efficient earth exploration in remote sensing. However, because of the limited spatial resolution, mixed pixels widely exist in the obtained hyperspectral data. It severely hinders the application of hyperspectral data. Hence, hyperspectral unmixing (HU) has become an essential task for HSI analysis. The most commonly model used for the mixture formation is a linear process or non-linear process. As linear mixing model (LMM) has clear physical meaning and is amenable to mathematical treatment, it has received widespread attention. To tackle the unmixing challenge, a number of linear algorithms have been proposed effectively. However, unmixing is a challenging, ill-posed inverse problem because of observation noise, environmental conditions, endmember variability, and data set size. The paper provided a comprehensive review of the state-of-the-art model in spectral unmixing. These models are discussed according to the following four categories: matrix decomposition, archetype analysis, bayesian method and sparse regression. In addition, both advantages and defects of these models are presented. Finally, a perspective on future research directions for advancing spectral unmixing methods is offered.