The study of Galois representations attached to elliptic curves is a very fruitful branch of number theory, which led to the solution of very tough problems, such as Fermat's Last Theorem. Given a rational elliptic curve E, the representation \rho_{E,p} is described by the action of the absolute Galois group of \mathbb{Q} on the p-torsion points of E. In 1972 Serre proved that for every rational elliptic curve E without CM there is a constant N_E such that, for every prime p>N_E, the Galois representation \rho_{E,p} is surjective. In the same article, he asked whether the constant N_E is independent of the curve, and this became known as Serre's Uniformity Question. In this talk, I will discuss the current progress towards the answer to this question, in particular the Runge method for modular curves, developed by Bilu and Parent, and the recent improvements obtained via this method by Le Fourn--Lemos and Lombardo and the speaker.