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Recent satellite missions have provided and continue to provide us with vast amounts of data on radiation measurements that generally present themselves as superpositions of various cosmological sources, most importantly cosmic microwave background (CMB) radiation and other galactic and extragalactic sources. We would like to obtain the estimates of these sources separately since they carry vital information of cosmological significance about our Universe. Although initial attempts to obtain sources have utilized blind estimation techniques, the presence of important astrophysical prior information and the demanding nature of the problem makes the use of informed techniques possible and indispensable. In this article, our objective is to present a formulation of the problem in Bayesian framework for the signal processing community and to provide a panorama of Bayesian source separation techniques for the estimation of cosmological components from the observation mixtures.