We describe the classification of irreducible admissible smooth representations of GL_n(Q_p) over an algebraically closed field of characteristic p, in terms of "supersingular" representations. This generalizes results of Barthel-Livne for n = 2. Our motivation is the hypothetical mod p Langlands correspondence for GL_n, which is supposed to relate smooth mod p representations of GL_n(Q_p) to n-dimensional mod p Galois representations.