Let e be a nilpotent element in a finite dimensional complex simple Lie algebra g and denote by g_e the centralizer of e in g. In my talk, based on recent joint work with Panyushev and Yakimova, I am going to present some results on the algebra A(e):=S(g_e)^ge of symmetric invariants of g_e. It turns out that in many cases A(e) is a graded polynomial algebra in l=rk(g) variables. For example, this holds for all nilpotent elements in g=gl(n) and g=sp(2n).