Central sequence algebras play an important role in C*-algebra and von Neumann algebra theory. 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 discuss the C*-theory version of central sequences 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.