Assuming the exchange of antiferromagnetic spin fluctuations as the Cooper pairing mechanism we calculate the doping dependence of the resonance peak seen in inelastic neutron scattering and the magnetic coherence effect. We find that the resonance peak in the magnetic susceptibility, Im χ(q,ω), appears only in the superconducting state at ωres and that it scales with Tc. Magnetic coherence is a result of an interplay between a d-wave order parameter and the kinematic gap ω0. We analyze the structure of Im χ below Tc, the doping dependence of ω0 and ωres, and the consequences for the optical conductivity.