We present recent results on quarkonium states from the Babar experiment. We have observed the Y(^3 1 D_J) state of bottomonium in the reaction Y(3S)->γ γ Y(^3 1D_J), γ(^3 1 D_J)->π π Y(1S) with a significance of 6.2 standard deviations. We present a study of the decay Y(1S)->D+* + X produced in the decay Y(2S)->π+ π- Y(1S) using a sample of 98.6 million Y(2S) events. We measure the Y(1S)=>D+* + X branching fraction and the momentum distribution of the D* in the Y(1S) rest-frame. We find evidence for an excess of D* production over the expected rate from the virtual photon annihilation process Y(1S)->γ*->cbar c->D+* X. We also present a search for the spin singlet h_b partner of the χb(1P) triplet, the h_b(1P) state of bottomonium in the transition Y(1S)->π0 h_b and Y(3s)->π+ π- h_b using a sample of 122 million Y(3S) events.