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In this talk, we review the mathematical optimization models for the Euclidean Steiner Tree Problem (ESTP) in $d$ dimensions proposed in the literature. The development of such models for the ESTP began in the late 1990s. The ESTP is a mixed integer nonlinear optimization problem with a history dating back to the 17th century. Several properties of its optimal solutions are well known, but it is still a big challenge to encode these properties in its modeling, aiming for its numerical resolution with branch-and-bound algorithms. We identify some of the difficulties and present the modeling techniques used in the literature to overcome them.