In this joint work with Vytautas Paskunas, we extend Colmez' results on locally algebraic vectors in the p-adic Langlands correspondence. The main result is the following: if p>3 and if Pi is a finite length admissible unitary Banach space representation of GL_2(Q_p), for which the locally algebraic vectors are dense in Pi, then the image of Pi by the Montreal functor is a potentially semi-stable p-adic Galois representation. We will explain how the theory of phi-gamma modules can be applied to prove this theorem.