The p-adic local Langlands aims to link representations of G(K), where G is a reductive group and K a p-adic local fields, with p-adic coefficients, and representations of the absolute galois group of K with same coefficients. Around the beginning of this millenium, the case of GL2(Qp) was ruled out and the other are still blurry. Focusing on p-torsion representations, we will give a point of vue on the emergence of such correspondance and state the simplest results. In particular, we will explain the first hints obtained by Breuil, then a core tool called Colmez's functor constructing Galois representation from GL2(Qp) ones via (?,?)-modules. In a second time, we will also describe from the angle of Breuil-Herzig-Hu-Morra-Schraen and Zábrádi's work the current picture for GLn(Qp).