The Pila-Wilkie Theorem states that the number of rational points on a transcendental set grow subpolynomially in terms of their height. In order to prove this influential result, one has to be able to parametrize sets in a precise way. Wilkie conjectured that the bound of the Pila-Wilkie theorem may be improved for sets that can be defined using the exponential function and polynomials. Earlier work of Pila showed that this is possible, given an even more delicate type of parametrization. My talk will survey on the role of parametrization in the Pila-Wilkie theorem and the current state of the art.