Hodge theory, as developed by Deligne and Griffiths, is one of the main tool for analyzing the geometry and arithmetic of complex algebraic varieties, that is, solution sets of algebraic equations over the complex numbers. It is an essential fact that at heart, Hodge theory is not algebraic but rather transcendent. I will try to describe how tame geometry, whose idea was introduced by Grothendieck in the 1980s and was developed by model theorist as o-minimal geometry, seems to be the natural framework to control this transcendence.