Yukawa systems are good representations of structures forming in dusty plasma and colloidal experiments. The potential is such systems is φ(r)=(q2/r) e-κr, instead of the simple Coulomb potential φ(r)=q2/r, where κ is the "screening parameter". Part of the theoretical work that has to be done in order to analyze experimental and simulation results on plasma crystals involves the understanding of the theoretical structure of phonon dispersion in Yukawa lattices and the relationship between these perfect lattice phonons on the one hand, and the excitations in the disordered and liquid states on the other. Earlier calculations of the excitation spectra of the two-dimensional (2D) and three-dimensional (3D) Yukawa liquids were based on the quasilocalized charge approximation (QLCA), whose implicit premise is that the spectrum of an average distribution is a good representation of the actual spectrum. We have numerically calculated the full phonon spectrum for 2D hexagonal Yukawa lattices, for a wide range of screening parameter values and along different propagation angles. For the finite temperature solid and liquid systems, Molecular Dynamics (MD) simulations have been performed, providing oscillation spectra of density and current fluctuations.