A central sequence in a $C^*$-algebra is a sequence (x\_n) of elements such that [x\_n, a] converges to zero, for any element a of the $C^*$-algebra. In von Neumann algebra setting one typically means the convergence with respect to tracial norms, while in $C^*$-theory it is with respect to the $C^*$-norm. In this talk we will consider the $C^*$-theory version of central sequences. We will discuss properties of central sequence algebras and in particular address a question of J. Phillips and of Ando and Kirchberg of which separable $C^*$-algebras have abelian central sequence algebras. \\ \\ Joint work with Dominic Enders.