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 ω_res and that it scales with T_c. Magnetic coherence is a result of an interplay between a d-wave order parameter and the kinematic gap ω_o. We analyze the structure of Im χ below T_c, the doping dependence of ω_o and ω_res, and the consequences for the optical conductivity.