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The initial sections of the paper give a concise presentation, speciallydesigned for a mathematically oriented audience, of some of the most basicfacts on the functional architecture of early vision. Such information isusually scattered in a variety of papers and books, which are not easilyaccessible by non-specialists. Our goal is thus to offer a handy and shortintroduction to this topics, which might be helpful for researchers willing toenter the area of the applications of modern Differential Geometry in studieson the visual systems, baptized neurogeometry by J. Petitot. We then offer asurvey of three of the most important neurogeometric models: Petitot's contactmodel of the primary visual cortex, its extension to A. Sarti, G. Citti and J.Petitot's symplectic model, and P. C. Bressloff and J. D. Cowan's sphericalmodel of hypercolumns. We finally discuss the main points of the so-called``conformal model'' for hypercolumns (a model that was briefly presented in [D.V. Alekseevsky, Conformal model of hypercolumns in V1 cortex and the Moebiusgroup, in ``Geometric science of information'', pp. 65--72, Springer, 2021] andgiven in detail in [D. V. Alekseevsky and A. Spiro, Conformal models forhypercolumns in the primary visual cortex V1, arXiv 2024]), which can beconsidered as a synthesis of the symplectic and the spherical models.

The functional architecture of the early vision and neurogeometric models