In a pioneering paper, Pila and Zannier showed how one can prove arithmetic results (the Manin-Mumford Conjecture) using transcendental methods (the Ax-lindemann conjecture). Their approach has since been greatly developed, and is a major ingredient in the Andre-Oort conjecture for Shimura varieties as well as the more general Zilber-Pink conjecture, that serves as a sort of flagship for the field of unlikely intersections. We'll explain this story and present a new result (joint with Pila and Mok) proving a general transcendence theorem known as Ax-Schanuel for arbitrary Shimura varieties.