We summarize our recent theoretical studies on the spin dynamics in th
e normal state of the metallic cuprates. The contrasting wave vector d
ependence of the dynamical spin structure factor S(q, omega) in LaSrCu
O and YBaCuO systems are attributed to the differences in the fermiolo
gy, in conjunction with strong Coulomb correlations. These effects are
found to account also for the anomalous temperature and frequency dep
endence of S(q, omega). We conclude that the low energy spin dynamics
of the metallic cuprates are described in terms of correlated quasipar
ticles with a Luttinger Fermi surface and a non-zero antiferromagnetic
exchange interaction.