The KdV hierarchy is a hierarchy of integrable equations generalizing the KdV equation. In this talk, we show that the whole hierarhcy is wellposed for initial data in H^{-1} on the line, while on the torus we have wellposedness in H^{N-2} for N-th KdV equation. The main ingredients include: (1) modified Muria map that relate the KdV hierarchy to the Gardner hierarchy; (2) the idea of approximate flow by Killip and Visan (3) Kato smoothing estimate for KdV hiearchy and the difference flow on the line. This is based on joint work with F. Klaus and H. Koch.