By a theorem of Borel and Harish-Chandra, an arithmetic group in a semisimple Lie group is a lattice. Conversely, by a celebrated theorem of Margulis, in a higher rank semisimple Lie group G any irreducible lattice is an arithmetic group. The aim of this lecture is to survey an arithmeticity criterium for discrete subgroups which are not assumed to be lattices. This criterium, obtained with Miquel, generalizes works of Selberg and Hee Oh and solves a conjecture of Margulis. It says: a discrete irreducible Zariski-dense subgroup of G that intersects cocompactly at least one