  The spin dynamics of high temperature superconductors measured by inelastic
neutron scattering is reviewed. The spin susceptibility evolves a lot with
increasing doping from the undoped insulating state to the overdoped metallic
state. In the superconducting state, a strong magnetic resonance peak occurs in
the spin excitation spectrum whose energy is proportional to the
superconducting temperature. In underdoped and optimally doped regimes, normal
state antiferromagnetic fluctuations are observed, proving the existence of
strong electronic correlations in cuprates. They are characterized by a spin
pseudo-gap. In contrast, these dynamical spin correlations vanish in overdoped
samples.
