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The formation of geometrical concepts is done differently than it is in the formation of arithmetical concepts. Regardless of this general statement, there are theories presented in this survey that describe the process of formation of geometrical concepts and geometrical reasoning. Research on the understanding of geometrical concepts has been grouped around two main issues: the understanding of geometrical figures and the functioning of these figures in space. The problem of understanding these figures, indicated by Van Hiele’s theory, is still worth considering and research has uncovered much information on how it takes place in children’s minds. In research on children’s understanding of regularity, one can distinguish a number of issues—from the very fact of their perception of the regularity by creating arrangements of surfaces to geometrical relations hidden in mosaics.