Probabilistic latent semantic analysis is a statistical technique developed for information retrieval and spanned many fields. It yields intuitive and solid results. However, the rigidity of the assumptions and the iterative nature derived from the Expectation-maximization algorithm generate several problems, dividing detractors and enthusiasts. In this manuscript, we first describe the Probabilistic latent semantic analysis. After, we discuss reformulations that attempt to solve these problems. We pay special attention to the works relating Probabilistic latent semantic analysis and the Singular value decomposition Theorem. Also, Probabilistic latent semantic analysis can be the basis for other techniques, such as kernelization or probabilistic transfer learning, and those that extend the descriptive character of the Principal component analysis to an inferential tool and open a window of opportunities.