Thanks to Langlands, we know the spectral decomposition of the space of functions which are $L^2$ (modulo center) on an arithmetical quotient for a reductive group, such as the group $GL(n)$ of invertible matrices, the group of orthogonal matrices, or of symplectic matrices... But this knowledge is only theoretical and requires the understanding of the irreducible subrepresentations in this space of functions; the sum of these irreducible subrepresentations is exactly what we call the discrete spectrum. The goal of this talk is to formulate  the concrete results that J. Arthur has obtained in order to describe this discrete spectrum for the classical groups.