Hyperspectral imaging belongs to a class of techniques called spectral imaging or spectral analysis. Image spectrometers are used to measure spectral radiation with high spectral resolution and produce spectral data in ten's or hundred's of bands called hyperspectral image. The objective of hyperspectral imaging is to find the spectrum for each pixel in the image of a scene, with the purpose of differentiating objects or materials. Due to low spatial resolution of hyperspectral images, sub-pixel mixing occurs on the surface leading to spectral mixtures. Spectral mixtures can be macroscopic or microscopic based on how the light interacts with the single or multiple surface materials. Mathematically, macroscopic spectral mixtures are modeled as linear and microscopic spectral mixtures are modeled as nonlinear. Hyperspectral unmixing is an emerging topic in hyperspectral image analysis to distinguish the materials present in an image and thereby finding the proportion of each material in an image. The distinct materials are called as end members and proportion values are called as abundance fractions. Hyperspectral image analyses are classified as supervised or unsupervised based on the prior knowledge of end members known or not. Linear spectral unmixing algorithms are based on pure pixel search, convex geometry and sparse regression approaches. The limitation of linear model is that it is not appropriate for real time implementation. The real physical interactions occurring between the light and material surface is not well addressed in linear model. Therefore, nonlinear models based on radiative transfer theory are preferred over simple linear models. Mathematical problems and potential solutions of the two models are analyzed in this paper. Hyperspectral unmixing can be extended for signal reconstruction, change detection, denoising and segmentation. In this paper, the state of the art methods in the literature have been analyzed through qualitative and quantitative measures with real images. © 2016 Pushpa Publishing House, Allahabad, India.