We present the first measurement of decay amplitudes in B-->phiK* and measurements of branching fractions in B-->phiK(*) decays based on 78.1 fb(-1) of data recorded at the Upsilon(4S) resonance with the Belle detector at the KEKB e+e- storage ring. The decay amplitudes for the different phiK*0 helicity states are measured from the angular distributions of final state particles in the transversity basis. The longitudinal and transverse complex amplitudes are |A0|2=0.43+/-0.09+/-0.04, |A(perpendicular)|2=0.41+/-0.10+/-0.04, arg((A(parallel))=-2.57+/-0.39+/-0.09, and arg((A(perpendicular))=0.48+/-0.32+/-0.06. The direct CP-violating asymmetries are found to be consistent with zero.