In this paper, the magnetoelectric (ME) coupling and working modes are defined and discussed. Several types of ME laminate composites based on Terfenol-D, Fe-Ga magnetostrictive layers and piezoelectric Pb(Mg1/3Nb2/3)O3-PbTiO3 crystal, Pb(Zr,Ti)O3 ceramic layers have been developed. Our experiments confirm that these ME composites have giant magnetoelectric voltage coefficients of ∼0.43×103 mV/Oe in the frequency range of 10-2<f<104 Hz under low magnetic bias. When operated under resonant conditions, the ME voltage coefficient is dramatically enhanced to maximum values as high as ∼20×103 mV/Oe. At resonance, our ME laminates have (i) a strong voltage gain effect; and (ii) an ultrahigh magnetic field sensitivity of near 10-12 Tesla.