Magnetic correlations in all four phases of pure and doped vanadium sesquioxide (V 2 O 3 ) have been examined by magnetic thermal-neutron scattering. Specifically, we have studied the antiferromagnetic and paramagnetic phases of metallic V 2Ϫy O 3 , the antiferromagnetic insulating and paramagnetic metallic phases of stoichiometric V 2 O 3 , and the antiferromagnetic and paramagnetic phases of insulating V 1.944 Cr 0.056 O 3 . While the antiferromagnetic insulator can be accounted for by a localized Heisenberg spin model, the long-range order in the antiferromagnetic metal is an incommensurate spin-density wave, resulting from a Fermi surface nesting instability. Spin dynamics in the strongly correlated metal are dominated by spin fluctuations with a ''single lobe'' spectrum in the Stoner electron-hole continuum. Furthermore, our results in metallic V 2 O 3 represent an unprecedentedly complete characterization of the spin fluctuations near a metallic quantum critical point, and provide quantitative support for the self-consistent renormalization theory for itinerant antiferromagnets in the small moment limit. Dynamic magnetic correlations for បϽk B T in the paramagnetic insulator carry substantial magnetic spectral weight. However, they are extremely short-ranged, extending only to the nearest neighbors. The phase transition to the antiferromagnetic insulator, from the paramagnetic metal and the paramagnetic insulator, introduces a sudden switching of magnetic correlations to a different spatial periodicity which indicates a sudden change in the underlying spin Hamiltonian. To describe this phase transition and also the unusual short-range order in the paramagnetic state, it seems necessary to take into account the orbital degrees of freedom associated with the degenerate d orbitals at the Fermi level in V 2 O 3 . ͓S0163-1829͑98͒06443-1͔