Our starting point is the Pila--Wilkie Theorem connecting o-minimality and diophantine geometry; this gives a wide class of `transcendental' sets for which there is a subpolynomial bound on the number of their rational points (or algebraic points of bounded degree) of bounded height. We will discuss the setting for this result as well as possible improvements to it, both instances in which the bound can be improved to a polylogarithmic one, and instances which bring effectivity in the original statement. Solutions to certain systems of differential equations, known as Pfaffian functions, will play a central role in both cases!