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This survey will appear in Vol. VII of the Hendbook of Teichm{\"u}ller theory(European Mathematical Society Publishing House, 2020). It is a commentary onTeichm{\"u}ller's paper "Einfache Beispiele zur Wertverteilungslehre",published in 1944, whose English translation appears in that volume. Togetherwith Teichm{\"u}ller's paper, we survey the development of value distributiontheory, in the period starting from Gauss's work on the Fundamental Theorem ofAlgebra and ending with the work of Teichm{\"u}ller. We mention thefoundational work of several mathematicians, including Picard, Laguerre,Poincar{\'e}, Hadamard, Borel, Montel, Valiron, and others, and we give a quickoverview of the various notions introduced by Nevanlinna and some of hisresults on that theory.

Value distribution theory and Teichm{\"u}ller's paper "Einfache Beispiele zur Wertverteilungslehre"