  We derive a characterization of the complex projective K3 surfaces which have
automorphisms of positive entropy in term of their N\'eron-Severi lattices.
Along the way, we classify the projective K3 surfaces of zero entropy with
infinite automorphism groups and we determine the projective K3 surfaces of
Picard number at least five with almost abelian automorphism groups, which
gives an answer to a long standing question of Nikulin.
